Is there anything in Jewish texts on a third gender or gender deviant persons?

Question

Are there any stories particularly on those who do not fit into the categories man or woman? Is this considered a sin?

Answer 1

There are indeed discussions in the Gemara (Talmud) of the tumtum, an androgynous, i.e., one with both male and female characteristics. The gemara is not judging whether this is good or bad, but is rather interested to understand how various laws apply to tumtums, e.g., can they get married with a male or female?

R Alfred Cohen wrote an article on this in the Journal of Halacha & Contemporary Society. See also here although I cannot vouch for that source.

If you are asking about people who are physiologically male of female but feel different, I am not aware that this has been addressed in classical sources (but would love to be corrected). In general, the Torah isn't concerned and doesn't judge how people feel but how they act. As such feeling different wouldn't be a sin, but actions that run contrary to Torah law would be.