Second-century writings in the Jewish Talmud (traditional laws and writings) give us talmudic evidence for the existence of Jesus, whose Hebrew name was Yeshua. As would be expected, since the rulers of the time were against Jesus, the citations are all on the negative side, nonetheless they serve as evidence he did exist.
On the eve of Passover Yeshu was hanged. For forty days before the execution took place, a herald went forth and cried, “He is going forth to be stoned because he has practiced sorcery and enticed Israel to apostasy. Any one who can say anything in his favour, let him come forward and plead on his behalf.” But since nothing was brought forward in his favour he was hanged on the eve of the Passover! – Ulla retorted: Do you suppose that he was one for whom a defence could be made? Was he not a _Mesith_ [enticer], concerning him Scripture says, _Neither shalt though spare, neither shalt thou conceal him?_ With Yeshu however it was different, for he was connected with the government for royalty [i.e., influential]. Our Rabbis taught: Yeshu had five disciples, Matthai, Nakai, Nezer, Buni, and Todah.
from Baraitha Bab. Sanhedrin 43a
“May our company not be like that of Elisha, from which issued Gehazi. _In our bread places_: may we produce no son or pupil who disgraces himself in public.” One manuscript (M) adds to the end of this saying, “like the Nazarene.”
from b. Berakot
“Jesus the Nazarene [who] practised magic and led Israel astray.”
from b. Sabbat 116b and b. Sanhedrin 107b