He didn't, he believed his (at them time) new girlfriend that she's infertile.

OP, you can't blame this just on his ex. He CHOSE to not wear condoms. He's to be blamed too.

We had a child because I believed I fixed him

You can't fix another person.

I started to parent his child and cook healthy stuff for him as well. I thought we could do this life thing together.

Together? You need to get away from this abuser.

It's not the first time he was abusive but I really want to be free in this one life I have and I can't do that with my daughter in shared custody.

Get professional help. Reach out to u/ebbie45, they're a crisis counselor.