Any Historical Sources That Dispute The Existence Of Jesus?

[Zavdiel]

Are there any early sources that dispute the existence of Jesus from the early period of Christianity from say around the 3rd to 5th century?

I'm not aware of any but I don't know a great deal about the subject.

In a word, no. The closest you can get are Docetic writers who said that Jesus appeared to have material existence, but was in fact a purely "spiritual" being. The Docetists made this philosophical move in order to reconcile belief in Jesus with their Gnostic outlook (simply put, that materiality is evil, and people's "immaterial souls" needed to be saved from it).

What you find instead in non-Christian (even anti-Christian) sources are arguments or comments about Jesus that presuppose his existence. For example, one of Celsus' arguments (since he was mentioned in another post) against the virgin birth was that Jesus' father was actually a soldier called Panthera. Origen quotes Celsus on this in this passage from Contra Celsum:

But let us now return to where the Jew is introduced, speaking of the mother of Jesus, and saying that "when she was pregnant she was turned out of doors by the carpenter to whom she had been betrothed, as having been guilty of adultery, and that she bore a child to a certain soldier named Panthera;" and let us see whether those who have blindly concocted these fables about the adultery of the Virgin with Panthera, and her rejection by the carpenter, did not invent these stories to overturn His miraculous conception by the Holy Ghost: for they could have falsified the history in a different manner, on account of its extremely miraculous character, and not have admitted, as it were against their will, that Jesus was born of no ordinary human marriage. It was to be expected, indeed, that those who would not believe the miraculous birth of Jesus would invent some falsehood. And their not doing this in a credible manner, but (their) preserving the fact that it was not by Joseph that the Virgin conceived Jesus, rendered the falsehood very palpable to those who can understand and detect such inventions.[1]

But this argument only makes sense if it is an alternative explanation of a really-existing Jesus - it makes no sense to argue against the virgin birth of a non-existent figure. The lack of ancient sources positively asserting or presupposing the non-existence of Jesus means that any defense of that belief today necessarily has to be, at most, based on an argument from silence (and very often, it has to be said, such defenses do not even rise to the level of argumentation). The obvious existence and coherence of ancient sources from both Christian and non-Christian sources making historical claims about Jesus, means that an argument from silence requires reasons to doubt the reliability of all these sources (whether textually or historically) before it can even get off the ground. The only way, it seems to me, to even be rationally agnostic about the existence of Jesus is to accept criteria for ancient historiography which cannot themselves be rationally held.

[1] Origen, Contra Celsum, Chapter XXXII. Notably, Origen argues on historical grounds - not theological or philosophical ones - reasons to accept the virgin birth.