18 & a FTM

I’m 18 & a ftm I’m currently 32 weeks + 3.. my babies father cheated on me all along and I didn’t know until about 2 weeks ago that I got into his stuff. Not to mention he would always start arguments and I figured that was the way he would do so he can be able to leave for the day & see whatever girl he would talk to. It wasn’t just 1 but about 7 girls. Now some of the messages I seenhim denying our baby to get to talk to other girls. This is his second baby as he has a kid with an ex. After seeing all that it had me thinking it truly broke my heart and I know it isn’t the babies fault but I’m to the point/ depression that I feel like I don’t want this baby anymore.. but then at times I know if I give her up I’ll regret it & my family would judge me.. when I told him about it he talked crap and said he won’t sign anything that he won’t give her up. To give her to him, but why? If he denied her just about my whole pregnancy.. I need advice please

Most of you guys said to not add him to the birth certificate but he did mention to me if I didn’t he’ll take me to court and tell them otherwise that he did want to be there and everything. But I do have prove of all the messages were he denied her??