Baby's daddy!

Lisa • 36 years old, first time mom after 7 years ttc, baby boy Colton born Aug. 23rd 👶. Lost 2nd baby at 7 weeks.
So I'm due in September with my first baby after 7 years of ttc. Baby's daddy is in denial that I'm carrying his child and has threatened to sue me if paternity test proves baby isn't his (which it is). He isn't part of this pregnancy and has said he will go for 50/50 custody because he doesn't want to pay child support. He has no real interest in being a dad. He gave up rights to his first 2 kids and let his sister adopt them. Just wish he'd sign his rights away with this child too. He's even talked of moving several states away. I'm afraid if he gets custody, he will take my baby out of state. No real question, just wanted to explain my situation.