I have a daughter who's father may not be her paternal father. We are undergoing paternity testing to determine paternity because her "alleged" father has become abusive and violent. He threatens me that if he isn't the father that he will still continue to be around and have rights is this true?

Absolutely not. If he is NOT the father he would have the same rights as your next door neighbor or the guy browsing the meat counter at your local grocery store.

The only people who have rights to a child are the biological parents.