Josephus recounted that Jesus healed Pilates wife of something.. don't remember what page in my version but remember reading that... Josephus was a non religious non christian Jew too, during that time.. as far as I know the only non believer evidence of Jesus healings..
Chapter 9 (“Ancient Non Christian Sources”) of Dr. Gary R. Habermas book “The Historical Jesus” has a quote on page 203. The footnote says: “The quotation was taken from the reading in ‘The Babylonain Talmud’ transl. By I. Epstein (London: Soncino, 1935), vol III, Sanhedrin 43a p281
The quote from Talmud 43a page 281 is:
On the eve of the 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 favor, let him come forward and plead on his behalf.” But since nothing was brought forward in his favor, he was hanged on the eve of Passover.
End of Quote
Dr. Habermas makes a few points, which include the following:
1. This is a brief account of the death of Jesus. It supports the fact he was crucified, and the time of the event. The term “hanged” was a less commonly used synonym for “crucified” at that time. (Gal. 3:13)
2. While the “40 days” is not specifically mentioned in the NT, this is consistent with Jewish practice as well as a reading of the threats against Jesus in John 8:58-59; 10:31-33, 39.
3. It’s the use of the word “sorcery” I thought you might find interesting. This account infers Jesus did perform miraculous acts, but attributed them to sorcery. Check out Mark 3:23-29 for a NT account of this charge.
4. Dr. Habermas makes many more interesting points. The one I found interesting is his comment that there is no explanation in this quote as to why Jesus was not stoned, but was hanged. I believe the answer is found in Gal 3:13 and the OT verse it quotes (Deuteronomy 21:23).
Hope this helps :)