What is needed to terminate fathers rights. If he just recently found out about this 6yr old little girl just had a paternity test. She is being raised by her mothers boyfriend since she was born was given his last name. Now her mother is taking my fiancé for child support claiming he is the father. The mother has harassed him several times in public has had the police called on her by people for this. He does not want to have any problems with them and would rather give up his rights to this child if it turns out he is the father. Can he do this?

No.

If he is indeed the father (A court-ordered paternity test would be the only reliable and legally binding way to tell for sure), termination of parental rights (if allowed) would not free him from his duty to pay child support. TPR is normally only ordered if the child is adopted, and in most places a boyfriend of the mother doesn't qualify. The boyfriend (again, in most places) must marry the mother in order to qualify for adoption.

There is this myth that a parent can just give up their rights. But its only a myth. Only a court can terminate rights and no court will do that to let a parent out of paying support.

He can have nothing to do with the child, but if it is his child he will have to support her unless she is adopted. He can ask the court to order her to stop harassing him and not contact him. But he will need to pay support.