i don't know if he existed but there is no evidence that he did...
for one he was supposed to be a Roman citizen since his at least registered as a father had a store (carpenter) and he had access in libraries (only roman citizens had privileges in education during that time) but there is nowhere a birth certificate to be found....
secondly romans where really typical with bureaucracy papers and mostly with executions and yet there is nowhere a paper of his execution (really weird if you think that they needed a written order from the king and with the stamp of the emperor to execute someone and after the execution the performer of the act had to write a full report of the time place and stuff'
i don't say he didn't exist at all but that we can't say for sure