Is he allowed to just sign over his rights without any responsibility and how likely am I to be awarded child support?

I dated a man who was married but continued to insist that he was either already divorced or in the process of the divorce. During our relationship, I became pregnant. At first he stated that he did not want the baby but he grew into it and even asked my father if he could marry me and was becoming excited about the baby. I was recently informed that he can sue me for entrapment and subpoena my medical records to see if I lied about being on birth control. He is now currently living in another state with his wife. Is any of this legitimate?