Scared and Protective Momma-to-be

My ex boyfriend and I just recently broke up. He was emotionally abusive, and a complete pathological liar. He believed I was cheating on him our entire relationship, no matter what I did to prove to him. I started cutting ties with friends and some family just for him. He ended up taking my phone and threw it, even pinning me down on our bed and yelling in my face.

I'm only in my first trimester, and I have a serious case of endometriosis, where doctors told me I would NEVER conceive.

I don't want to get an abortion, but I don't want him coming anywhere near this baby. He is also an alcoholic with serious anger issues.

I'm scared that he will try to come after me and try to take the baby from me. So I'm not going to post any pictures or ANYTHING on social media about my pregnancy or even of the baby within the first few months.

I talked to my NP today at my appointment, and she said that he can't legally sign the birth certificate anyways because we aren't married or never were, but there are paternity rights.

I'm not with him and I never will be again, what's the legal stuff with him not signing the paternity rights? Could I just say that the father isn't in my life and that's it? Or would there be a certain period of time where he could try and attest it legally? I don't know. I'm just scared. I live in NY if that helps with any laws that there are.

Thanks.