Josephus didn't write any passages at all about Christians or John the Baptist, every word, and in some cases the entire surrounding chapter, were interpolated by pious christian scribes who found irresistible the urge to "correct" the most famous of historians (for Christians even then) who surely had to know about James and John and Jesus.
The first and most glaring is Antiquities 18.3.3 where seeing the story of Pilate in 18.3.2 having Roman soldiers fall upon and kill unarmed Jews protesting his use of sacred money to pay for a project to bring water to Jerusalem, a Christian writer found it a suitable spot to add his text about Jesus
Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Greeks. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, those that loved him at the first did not forsake him; for he appeared to them alive again the third day; as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day.
Γίνεται δὲ κατὰ τοῦτον τὸν χρόνον Ἰησοῦς σοφὸς ἀνήρ, εἴγε ἄνδρα αὐτὸν λέγειν χρή· ἦν γὰρ παραδόξων ἔργων ποιητής, διδάσκαλος ἀνθρώπων τῶν ἡδονῇ τἀληθῆ δεχομένων, καὶ πολλοὺς μὲν Ἰουδαίους, πολλοὺς δὲ καὶ τοῦ Ἑλληνικοῦ ἐπηγάγετο· ὁ Χριστὸς οὗτος ἦν. καὶ αὐτὸν ἐνδείξει τῶν πρώτων ἀνδρῶν παρ᾽ ἡμῖν σταυρῷ ἐπιτετιμηκότος Πιλάτου οὐκ ἐπαύσαντο οἱ τὸ πρῶτον ἀγαπήσαντες· ἐφάνη γὰρ αὐτοῖς τρίτην ἔχων ἡμέραν πάλιν ζῶν τῶν θείων προφητῶν ταῦτά τε καὶ ἄλλα μυρία περὶ αὐτοῦ θαυμάσια εἰρηκότων. εἰς ἔτι τε νῦν τῶν Χριστιανῶν ἀπὸ τοῦδε ὠνομασμένον οὐκ ἐπέλιπε τὸ φῦλον.This insertion has been picked to pieces by others, and is almost universally regarded as an insertion already, so I will simply hit a few key points. First this is a digression about Jesus, which is has follow up in the subsequent passages. Instead they up pick on the growing dissent and disorder among the Jews from dealing with the Romans, also dealt with in the material prior to the insertion, telling now the tail of the practices of the temple of Isis in Rome and how certain virtuous married woman named Paulina was the object of obsession of one Decus Mundus. There is simply no connection of this passage about Jesus to the surrounding material and it can be dispensed with at no effect.
Secondary issues with the passage have to deal with its creedal nature. Somehow this devote Jew declares this Jesus the messiah (ὁ Χριστὸς οὗτος ἦν) which is beyond absurd; it is an example of how the pious Christian scribe, who clearly revered Josephus, could not resist giving proof of his Christian sympathies, giving away the source of the insertion in the process. The completeness of the confession is the statement that Christ appeared alive again after three days as foretold by the prophets, based heavily upon the Catholic version of 1 Corinthians 15:3-4 and the Gospels accounts. This also contradicts directly Origin (Commentary on Matthew 10.17) who knows nothing of this insertion, but does know the comments about James, says that Josephus "did not accept Jesus as Christ."
Then there is the post-Pauline reconciliation theme of Jews and Greeks both being Christians (καὶ πολλοὺς μὲν Ἰουδαίους, πολλοὺς δὲ καὶ τοῦ Ἑλληνικοῦ ἐπηγάγετο), a post Gospel Pauline theme that contradicts the mission of Jesus portrayed in the Gospels is present, which hints that this passage dates from after the Pauline Epistles had circulated widely - something that is generally thought to be the middle of the 2nd century, even by conservative scholars. Another indication that this is from the 3rd century (besides being unknown by Origin) is boast of a Christian tribe, something that should not have existed separate in any size from the Jews when Josephus was writing in the later quarter of the 1st century. That is enough for me.
A more detailed analysis of this passage and its dependence upon Luke's Emmaus sequence by Dr. Gary Goldberg, The Journal for the Study of the Pseudepigrapha 13 (1995) pp. 59-77, the can be found following this link on the Josephus.org website.
The second Christian insertion concerns John The Baptist in Antiquities 18.5.2 shown here
Now some of the Jews thought that the destruction of Herod's army came from God, and that very justly, as a punishment of what he did against John, that was called the Baptist: for Herod slew him, who was a good man, and commanded the Jews to exercise virtue, both as to righteousness towards one another, and piety towards God, and so to come to baptism; for that the washing [with water] would be acceptable to him, if they made use of it, not in order to the putting away [or the remission] of some sins [only], but for the purification of the body; supposing still that the soul was thoroughly purified beforehand by righteousness. Now when [many] others came in crowds about him, for they were very greatly moved [or pleased] by hearing his words, Herod, who feared lest the great influence John had over the people might put it into his power and inclination to raise a rebellion, (for they seemed ready to do anything he should advise,) thought it best, by putting him to death, to prevent any mischief he might cause, and not bring himself into difficulties, by sparing a man who might make him repent of it when it would be too late. Accordingly he was sent a prisoner, out of Herod's suspicious temper, to Macherus, the castle I before mentioned, and was there put to death. Now the Jews had an opinion that the destruction of this army was sent as a punishment upon Herod, and a mark of God's displeasure to him.Ostentatiously this passage attempts to place the blame for the destruction of a Jewish army under Herod against Aretas over divorcing his daughter to take up with Herodias. This mostly happened it seems from the account by treachery when the the soldiers under Philip went over to Aretas. The mention of the Herodias and Herod reminded our Christian editor of the story of John's opposition to Herod marrying Herodias from Luke 3:19-20, (strangely garbled to be Herod's brother Philip who is married to Herodias in the version from Matthew 14:3-11/Mark 6:17-28). The account is suspicious because we are told, backhandedly that John's baptism is for the remission of sin because the Jews washing is not (μὴ ἐπί τινων ἁμαρτάδων παραιτήσει χρωμένων) but instead for the purification of the body. This is followed strangely by a need to say in a disapproving voice that the Jew suppose the soul is purified beforehand by righteousness, which is inconsistent with his other statements on the soul.
Τισὶ δὲ τῶν Ἰουδαίων ἐδόκει ὀλωλέναι τὸν Ἡρώδου στρατὸν ὑπὸ τοῦ θεοῦ καὶ μάλα δικαίως τινυμένου κατὰ ποινὴν Ἰωάννου τοῦ ἐπικαλουμένου βαπτιστοῦ. κτείνει γὰρ δὴ τοῦτον Ἡρώδης ἀγαθὸν ἄνδρα καὶ τοῖς Ἰουδαίοις κελεύοντα ἀρετὴν ἐπασκοῦσιν καὶ τὰ πρὸς ἀλλήλους δικαιοσύνῃ καὶ πρὸς τὸν θεὸν εὐσεβείᾳ χρωμένοις βαπτισμῷ συνιέναι· οὕτω γὰρ δὴ καὶ τὴν βάπτισιν ἀποδεκτὴν αὐτῷ φανεῖσθαι μὴ ἐπί τινων ἁμαρτάδων παραιτήσει χρωμένων, ἀλλ᾽ ἐφ᾽ ἁγνείᾳ τοῦ σώματος, ἅτε δὴ καὶ τῆς ψυχῆς δικαιοσύνῃ προεκκεκαθαρμένης. καὶ τῶν ἄλλων συστρεφομένων, καὶ γὰρ ἥσθησαν ἐπὶ πλεῖστον τῇ ἀκροάσει τῶν λόγων, δείσας Ἡρώδης τὸ ἐπὶ τοσόνδε πιθανὸν αὐτοῦ τοῖς ἀνθρώποις μὴ ἐπὶ ἀποστάσει τινὶ φέροι, πάντα γὰρ ἐῴκεσαν συμβουλῇ τῇ ἐκείνου πράξοντες, πολὺ κρεῖττον ἡγεῖται πρίν τι νεώτερον ἐξ αὐτοῦ γενέσθαι προλαβὼν ἀνελεῖν τοῦ μεταβολῆς γενομένης μὴ εἰς πράγματα ἐμπεσὼν μετανοεῖν. καὶ ὁ μὲν ὑποψίᾳ τῇ Ἡρώδου δέσμιος εἰς τὸν Μαχαιροῦντα πεμφθεὶς τὸ προειρημένον φρούριον ταύτῃ κτίννυται. τοῖς δὲ Ἰουδαίοις δόξαν ἐπὶ τιμωρίᾳ τῇ ἐκείνου τὸν ὄλεθρον ἐπὶ τῷ στρατεύματι γενέσθαι τοῦ θεοῦ κακῶσαι Ἡρώδην θέλοντος.
But it is the external evidence that convicts the entire passage. It is a digression that introduces a Gospel story, and intrudes upon the actual story, which ends 18.5.1 with Vitellius dispatched by Tiberius to deal with Aretas, and then picks up in 18.5.3 exactly where it left off with Vitellius readying to make war with Aretas. The same characters, with no reference to John or his death, as you can see.
[18.5.1] ... So Aretas made this the first occasion of his enmity between him and Herod, who had also some quarrel with him about their limits at the country of Gamalitis. So they raised armies on both sides, and prepared for war, and sent their generals to fight instead of themselves; and when they had joined battle, all Herod's army was destroyed by the treachery of some fugitives, who, though they were of the tetrarchy of Philip, joined with Aretas's army. So Herod wrote about these affairs to Tiberius, who being very angry at the attempt made by Aretas, wrote to Vitellius to make war upon him, and either to take him alive, and bring him to him in bonds, or to kill him, and send him his head. This was the charge that Tiberius gave to the president of Syria.
[18.5.3] So Vitellius prepared to make war with Aretas, having with him two legions of armed men; he also took with him all those of light armature, and of the horsemen which belonged to them, and were drawn out of those kingdoms which were under the Romans, and made haste for Petra, and came to Ptolemais. But as he was marching very busily, and leading his army through Judea, the principal men met him, and desired that he would not thus march through their land; for that the laws of their country would not permit them to overlook those images which were brought into it, of which there were a great many in their ensigns; so he was persuaded by what they said, and changed that resolution of his which he had before taken in this matter. Whereupon he ordered the army to march along the great plain, while he himself, with Herod the tetrarch and his friends, went up to Jerusalem to offer sacrifice to God, an ancient festival of the Jews being then just approaching; and when he had been there, and been honorably entertained by the multitude of the Jews, he made a stay there for three days, within which time he deprived Jonathan of the high priesthood, and gave it to his brother Theophilus. But when on the fourth day letters came to him, which informed him of the death of Tiberius, he obliged the multitude to take an oath of fidelity to Caius; he also recalled his army, and made them every one go home, and take their winter quarters there, since, upon the devolution of the empire upon Caius, he had not the like authority of making this war which he had before...The Third Christian interpolation occurs in 20.9.1 which adds the death of James the bother of Jesus called Christ, describing it as done by a rogue Jewish sanhedrim called by the Ananus - who is described as a member of the Sadduccees in the passage below:
Antiquitates Iudaice libri XX, De bello Iudaico libri VIIAnd now Caesar, upon hearing the death of Festus, sent Albinus into Judea, as procurator. But the king deprived Joseph of the high priesthood, and bestowed the succession to that dignity on the son of Ananus, who was also himself called Ananus. Now the report goes that this eldest Ananus proved a most fortunate man; for he had five sons who had all performed the office of a high priest to God, and who had himself enjoyed that dignity a long time formerly, which had never happened to any other of our high priests. But this younger Ananus, who, as we have told you already, took the high priesthood, was a bold man in his temper, and very insolent; he was also of the sect of the Sadducees, who are very rigid in judging offenders, above all the rest of the Jews, as we have already observed; when, therefore, Ananus was of this disposition, he thought he had now a proper opportunity [to exercise his authority]. Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrim without his consent. Whereupon Ananus complied with what they said, and wrote in anger to Albinus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood.
Πέμπει δὲ Καῖσαρ Ἀλβῖνον εἰς τὴν Ἰουδαίαν ἔπαρχον Φήστου τὴν τελευτὴν πυθόμενος. ὁ δὲ βασιλεὺς ἀφείλετο μὲν τὸν Ἰώσηπον τὴν ἱερωσύνην, τῷ δὲ Ἀνάνου παιδὶ καὶ αὐτῷ Ἀνάνῳ λεγομένῳ τὴν διαδοχὴν τῆς ἀρχῆς ἔδωκεν. τοῦτον δέ φασι τὸν πρεσβύτατον Ἄνανον εὐτυχέστατον γενέσθαι: πέντε γὰρ ἔσχε παῖδας καὶ τούτους πάντας συνέβη ἀρχιερατεῦσαι τῷ θεῷ, αὐτὸς πρότερος τῆς τιμῆς ἐπὶ πλεῖστον ἀπολαύσας, ὅπερ οὐδενὶ συνέβη τῶν παρ᾽ ἡμῖν ἀρχιερέων. ὁ δὲ νεώτερος Ἄνανος, ὃν τὴν ἀρχιερωσύνην ἔφαμεν εἰληφέναι, θρασὺς ἦν τὸν τρόπον καὶ τολμητὴς διαφερόντως, αἵρεσιν δὲ μετῄει τὴν Σαδδουκαίων, οἵπερ εἰσὶ περὶ τὰς κρίσεις ὠμοὶ παρὰ πάντας τοὺς Ἰουδαίους, καθὼς ἤδη δεδηλώκαμεν. ἅτε δὴ οὖν τοιοῦτος ὢν ὁ Ἄνανος, νομίσας ἔχειν καιρὸν ἐπιτήδειον διὰ τὸ τεθνάναι μὲν Φῆστον, Ἀλβῖνον δ᾽ ἔτι κατὰ τὴν ὁδὸν ὑπάρχειν, καθίζει συνέδριον κριτῶν καὶ παραγαγὼν εἰς αὐτὸ τὸν ἀδελφὸν Ἰησοῦ τοῦ λεγομένου Χριστοῦ, Ἰάκωβος ὄνομα αὐτῷ, καί τινας ἑτέρους, ὡς παρανομησάντων κατηγορίαν ποιησάμενος παρέδωκε λευσθησομένους. ὅσοι δὲ ἐδόκουν ἐπιεικέστατοι τῶν κατὰ τὴν πόλιν εἶναι καὶ περὶ τοὺς νόμους ἀκριβεῖς βαρέως ἤνεγκαν ἐπὶ τούτῳ καὶ πέμπουσιν πρὸς τὸν βασιλέα κρύφα παρακαλοῦντες αὐτὸν ἐπιστεῖλαι τῷ Ἀνάνῳ μηκέτι τοιαῦτα πράσσειν: μηδὲ γὰρ τὸ πρῶτον ὀρθῶς αὐτὸν πεποιηκέναι. τινὲς δ᾽ αὐτῶν καὶ τὸν Ἀλβῖνον ὑπαντιάζουσιν ἀπὸ τῆς Ἀλεξανδρείας ὁδοιποροῦντα καὶ διδάσκουσιν, ὡς οὐκ ἐξὸν ἦν Ἀνάνῳ χωρὶς τῆς ἐκείνου γνώμης καθίσαι συνέδριον. Ἀλβῖνος δὲ πεισθεὶς τοῖς λεγομένοις γράφει μετ᾽ ὀργῆς τῷ Ἀνάνῳ λήψεσθαι παρ᾽ αὐτοῦ δίκας ἀπειλῶν. καὶ ὁ βασιλεὺς Ἀγρίππας διὰ τοῦτο τὴν Ἀρχιερωσύνην ἀφελόμενος αὐτὸν ἄρξαντα μῆνας τρεῖς Ἰησοῦν τὸν τοῦ Δαμναίου κατέστησεν.If you ignore the interpolation in blue, it becomes clear that Josephus is bringing up the indignation at Ananus for overstepping his bounds and calling a Sanhedrin, which is like convening an assembly or legislature into session. By this time in the Roman Empire the Sanhedrin was essentially a provincial council. While it can take on trials, by and large it is a patronage distributing council, and part time legislature. Wealthy people would buy their membership, and use it to gain advantage in contracts, settling disputes, allocating land and other largess. While nominally lead by the High Priest, a position sold that brings revenue to the Procurator.
Calling up judges (κριτῶν) makes no sense. The body judges like a Senate, with its members. There is no record or instance in the literature - beyond the Gospel accounts and Acts - that I am aware of for their ever being a Council of Judges or "supreme court" separate from the sanhedrim or some special subgroup within it. The members of the Sanhedrin were people of standing who worked most of the year, and would be in session only part time, much like say the Texas Legislature today, or the then contemporary Roman Senate.
The interpolation(s) very much obscures this point. Also calling James the brother of Jesus, here meant in a literal sense, is something more likely developed later as with the appearance of the epistle of James which is not mentioned by the Church fathers until the 3rd century, when the story of James becomes popular Apocrypha built upon Acts account. Also an extraneous and questionable charge that Ananus was a Sadduccee (note, the position was "up for bid" every few years, and it has been thought many if not most families that had high priests were in fact Sadduccees, nothing unique or different here), and speaking of Jews as other than Josephus' own group that they were more strict on judgment. What is striking is the contradiction to Josephus' comments of the Sadducces, that they are badly out number and unable to ever do anything even when they have a high priest and give in to the numbers and force of the Pharisees (Antiquities 18.2.4), and that they quarrel among themselves and so are ineffective (War 2.8.14). The idea that the Sadduccees could suddenly be effective in calling a sanhedrim - even as some race off to find Albinus-, and one to trial minor figures and execute them is completely different than the picture given elsewhere. There is also little reason to assume Ananus was a member, his behavior is explained well enough, being bold in temper and insolent (θρασὺς ἦν τὸν τρόπον καὶ τολμητὴς διαφερόντως).
This judgment has nothing to do with the report at hand nor was it the reason for Ananus getting sacked. He usurping powers not proscribed for the position he held. This point is almost lost with the digression into sect of the Sadducces and the supposed trial of James. The interpolation appears to be known by Origen when he wrote in the middle of the 3rd century. It has characteristics of the account of James in Acts and the rise in his stature per the epistle in his name. We can thus safely bound the interpolation in the early 3rd century.
All of these insertions have been covered by other scholars better. But the only point I wish to make is all the Christian statements are interpolations. There is no small kernel of authentic text, nothing. Josephus is not a witness. Christian writers had modified the text already before the middle of the 3rd century, at least the copies Origen saw, and probably the Jesus passage in 18.3.3 sometime near the beginning of the 4th century.
But I rank this less serious a problem than the interpolations in the Church Fathers since this forces us to to question the witnesses we want to most consider reliable. Unfortunately we cannot take that for granted.