Save up and get a good lawyer. Really.
I know we all want to poo poo his threats, but the court system doesn't just vary state by state, it varies county by county. The county I live in, he could walk out of jail and have 50/50 custody 3-6 months later. One county over, not so much.
If he can't sign the paternity papers, he can't be on the birth certificate, here in CA. is that how it is where you are?
The first steps you take in a custody case are the most important. It is very hard to get something back in court once you have lost it. You will not be able to cut him out completely if he (or his family) really wants to be involved. If his family has money you can get screwed.
So minimize the possible damage as soon as possible, get a good lawyer, not a cheap one. I don't care if you have the money, find it. Beg borrow steal. This is your child we are talking about. Until he gets it together keep him as far away as possible.