Has anyone gone through a custody battle in Ny state?

Im currently pregnant with my second child from the same father as my two year old daughter. Since we’ve found out I am pregnant I have since moved out of his apartment and back with my parents, we don’t really talk anymore. he’s always lacked supporting our child and is extremely mentally abusive towards me and on a couple occasions has become handsy, even broke my nose once but I didn’t report it. Due to how he acts and the things that have happened, I’ve always been afraid to take him to court for custody or child support. I’m just wondering if anyone has been through the same thing and can tell me how their experience went in court. Please and thank you