The Father Of My Child Says That He'll Sue For Custody If Anything Happens To Me Before He Signs Away Rights.

I'm currently 13 weeks pregnant as of today. The father of this child and I aren't married. He has said over and over he will be signing away his rights once they're born. When I told him I would be naming my best friend as the guardian of this child if something were to happen to me, he got upset and said that he "doesn't even know her" and that if I die in childbirth or any time before he signs his rights away that he would fight to take custody.

My best friend has already agreed to be the guardian if anything happens to me. I'll be putting this in my will. I've known her for several years, she's been extremely supportive and helpful throughout this pregnancy. She is in a stable long term relationship with a good job she's had for a few years now, a house she's renting with her fiance, is in a good mental state, and has the financial means and ability to care for my child.

The child's father is currently living with his parents, who are constantly threatening to kick him out for not finding a job, has had no job for over 2 years at this point, and isn't very mentally stable, although he is in therapy. He has no way to provide for this child if he were to get custody and no place for it to live if he were to be removed from his parents home. Does he even have a case for getting custody outside of the fact he's the father?