My daughter has a 6 week old son by a guy she had a casual sexual relationship. The father has not contributed anything in the support of this child. All he has done is come to the hospital the day after his birth to get a saliva sample for a DNA test through the mail. Turns out it is his child and he does not want to support it or see it. This is fine with her as she has a boyfriend who would one day adopt. The father is not on the birth certificate either. He keeps calling my daughter and upsetting her telling her to get a lawyer and he will not sign over his rights unless she is married. She can not afford a lawyer. She would rather have nothing further to do with this guy. I tell her he is just a control freak who wants to hassle her and if she ignores him he will go away. I say all the cards are in her hand because if they go to court he would have to pay child support and her hospital bill which was covered by Medical. She does not want to share this baby with him and he does not want to even see it. Can he sign over his rights if she is not married to her boyfriend in California and what could be his next step if she ignored his calls?

If his name is not on the birth certificate he has N0 rights so the deck IS stacked against him.

The babies father has no rights until he goes to court and asks for them, But he does have the right to go to court and get rights,

If he wants an attorney so bad let him get one

Most likely no, he cannot just sign his rights away, and even if he did, it would not stop his responsibility to pay child support.

He is in troubel on two fronts, one if she is on government assistance, they will go after the father of the child for the medical bills. She may as well file for child support and get the baby the money.
After he is having to pay support, if latter she wants him to sign over rights to adopt, knowing the child support will end then, he will be much more willing to sign them

Right now what 'rights' does he have since he never signed the birth certificate?
He can not sign over rights he doesn't even have.
I think you are right it is idle threats.