Can ex get visitation? if so how?

me and my ex split when i was six months pregnant because he was sending nude pics and recieving them from his ex (among other things but that was what basically ended it). so he moved out and i still tried to keep him included in the pregnancy because i didnt want to be selfish in anyway because its not the babys fault we broke up. however after about two weeks he said we should stop talking. and about a week later i txted him and ask if he wanted to work some agreement out so he could see his daughter. and he said he loved his daughter and would fight for her and hed see me in court. he has spent maybe a total of 80 dollars on things for her. whereas me and my family have spent near 800 including medical bills and having to go to the hospital twice. im having a complicated pregnancy and have to go to the dr. 3 times a month, and my daughter will be a premie because i have a short cervix. ive been on bedrest for 9 weeks now. he never asks about how the baby or pregnancy is going. he wont be at the hospital and wont be listed on the birth certificate. does it sound like hell get paternity established and pay child support so he can see her? i once asked for 40 dollars for a few things for the nursery and he said no. he lives with his mom, has no car or license. i dont regret my daughter in anyway i love her with all my heart and have been so scared id lose her throughout my pregnancy, im worried now he may go for visitation. hes not a good person and has continuously picked himself over her and i think its so disgusting. he also has a new gf so im hoping he will just get busy with that and stuff. he only makes 80 dollars a week as of now but from what i hear is trying to get another job. am i worried for nothing?