Fathers rights

So I’m currently 36 weeks pregnant. My ex recently left me while pregnant and kicked me out . I’ve had a really rough pregnancy it’s my first kid but not his he has 2 daughters from a previous relationship. Since I got pregnant he never helped me out financially . He never tried to help me out while pregnant I had to work up to 9 months because I had no type of help . He’s 26 unemployed and he also doesn’t give his daughters any type of financial support. His ex put him on child support and he won’t pay and she won’t make him pay what he owes . Also he got back with her she has also caused me drama in the past he disrespected my unborn baby and has shown that he doesn’t like my baby . She’s currently living with him and I don’t want her around my baby for those reasons. I also don’t want my baby to have his fathers last name so he doesn’t have any rights . I did tell him that I would let him see his baby whenever he wants and I won’t take him to court but I just don’t want him to have any rights . When I give birth he won’t be there so he won’t be on the birth certificate. He’s a narcissist and he’s not a good person he doesn’t work and he’s very unstable he also drinks a lot and gets aggressive. One time he got really mad and shoved/pushed me against the wall and left me all bruised up I took pictures of it . I still want him to be in my sons life regardless of how our relationship ended I just don’t want him to have rights. But I found out he wants to take me to court to fight for his rights as well . I know they have to do a DNA test and all but I’m wondering if they’ll let him have rights? I also don’t want him to take the baby to his house until he’s at least 1 since he’s a baby and needs full attention and I’m going to breast feed him . He has 2 daughters which he can’t even watch on his own . I need some advice and help. Also if he does get rights and I want him to pay child support how would he if he doesn’t have any type of income ? Can they force him to pay ?