Pseudo-Hegesippus writing about 370 CE is the earliest post-Eusebian witness to Josephus' supposed account of Jesus (the TF).
. They indeed paid the punishments of their crimes, who after they had crucified Jesus the judge of divine matters, afterwards even persecuted his disciples. However a great part of the Jews, and very many of the gentiles believed in him, since they were attracted by his moral precepts, by works beyond human capability flowing forth. For whom not even his death put an end to their faith and gratitude, on the contrary it increased their devotion. And so they brought in murderous bands and conducted the originator of life to Pilatus to be killed, they began to press the reluctant judge. In which however Pilatus is not absolved, but the madness of the Jews is piled up, because he was not obliged to judge, whom not at all guilty he had arrested, nor to double the sacrilege to this murder, that by those he should be killed who had offered himself to redeem and heal them. About which the Jews themselves bear witness, Josephus a writer of histories saying, that there was in that time a wise man, if it is proper however, he said, to call a man the creator of marvelous works, who appeared living to his disciples after three days of his death in accordance with the writings of the prophets, who prophesied both this and innumerable other things full of miracles about him. [p. 164] from which began the community of Christians and penetrated into every tribe of men nor has any nation of the Roman world remained, which was left without worship of him. If the Jews don't believe us, they should believe their own people. Josephus said this, whom they themselves think very great, but it is so that he was in his own self who spoke the truth otherwise in mind, so that he did not believe his own words. But he spoke because of loyalty to history, because he thought it a sin to deceive, he did not believe because of stubbornness of heart and the intention of treachery. He does not however prejudge the truth because he did not believe but he added more to his testimony, because although disbelieving and unwilling he did not refuse.
Rereading this I noted two things:
i/ There is no mention or allusion in the paraphrase of Josephus to the clause about Jesus he was the Christ
ii/ There is a strong emphasis on Josephus being an unbeliever in Christ and hence allegedly a particularly convincing witness. (An early example of the criteria of embarrassment !)
Put together this seems to require that the version of the TF known to pseudo-Hegesippus either omitted he was the Christ entirely or (IMO less likely) had he was the so-called Christ or some variant. If the text of the TF known to the author had read he was the Christ then it is likely that he would have alluded to it and improbable that he would have been so confident that Josephus was an unbeliever reluctantly bearing witness to the truth.
a/ Am I right on the specific point of the text of the TF known to pseudo-Hegesippus ?
b/ If so what implications does this have for the history of the TF ?