Separated, but my wife had a baby with someone else. Am I responsible for the child?

No it should not affect you at all. She will have to have a paternity test to prove you are not the father of the child. If I were you I would have a good attorney; or speak with the judge and make him aware at the time. As well you should ensure that she has not given the child your last name; since it is legally her last name she is still married to you. Good luck.