Pregnant and alone

I’m currently 8 months pregnant and my baby father has yet to get the baby anything he did send me money twice but to me that’s not enough he claims to be working hard for the baby and that’s why he’s never around or he will have excuses about his car ! I have still yet seen anything he has bought her I get the baby things every chance I get i dont even really need a baby shower bc I’ve got her basically everything I don’t understand why he doesn’t want to shop for her ik this is his 3rd baby (2 with someone else ) but why don’t u seem that interest in your 3rd and it’s like he cares about the baby so he says but his actions doesn’t show he cares about me I feel so selfish saying that but how do u care about her and not me and I’m the one carrying this baby ! I have did everything alone basically I put up her crib folded her clothes bought things went to appointments alone he’s only been to my very first one and my 20 week scan !! I said all this to say this SHOULD I ALLOW THIS MAN TO SIGN THE BIRTH CERTIFICATE! I feel like if u haven’t been a father this whole time bc it starts when you’re pregnant not once the baby is here he doesn’t deserve to sign it ! I honestly don’t want him to have any rights to her until we have something done in court bc I don’t want him trying to take her or anything (I have ptsd from my other baby father) but then I feel bad bc he is her father I’m just trying to protect my baby and me losing her !! Please help ! (Only nice comments please I’m already going through it )😪😭