There is a "Yeshu" mentioned in the Talmud who is criticized.

The Rosh [Asher] wrote that that does not refer to Jesus. [The Rosh was a Rishon]. The "Yeshu" mentioned in the Talmud was a disciple of one of the middle "zuggot' pairs mention in Pirkei Avot. [Yehoshua ben Perachia] So that is right in the middle of the second Temple. That is about 150 years before Jesus. Yeshu was not an uncommon name. [Where the Rosh wrote this? I seem to recall seeing it at the end of Gitten but maybe it was somewhere else.]

I mean to say the Talmud says openly exactly who it is referring to--that is the disciple of Yehushua ben Perachia. That means it can not be referring to the Yeshua of the NT.

I might just add the point that "Hagada" even in the Talmud itself is not binding. The idea of the Talmud is to get to the laws of Torah, not stories. That is not to say that the stories are not interesting. Interesting yes but fundamental and binding? No. As the Ramban and other Rishonim already made this point long ago.

I know people think Torah is all about interesting stories. But in fact it is not. It is about laws.