Legal advise? HELP!!!

So I’m currently 25 weeks pregnant and I’ve been doing this alone so far with the help of May mother. The dad has not given any money whatsoever and has not been apart of her this entire pregnancy. I’ve been buying everything that she needs. I told him the other day that after she is born I plan to file for child support. That is when he comes out of nowhere saying that he wants full custody. He makes way more money than me and has his own house but he lives down south and I live north of California. I have a full time job, own a house, and have transportation. I’m freaking out because he wants to take me to court. Does he have a chance? I’m scared and sorry if this is all over the place I’m just in a really bad place right now emotionally (since he told me this). And not only that but that his family back him up on this.

UPDATE: we were never married. We dated a year ago and then after I became pregnant. And he wants to have his last name on the certificate which I plainly said no. And we both live in California. I’ll have to seek out legal advise this week.