Can the father of my child sue for paternal rights?

I was dating a guy for about 2 months when I found out he had been cheating the whole time, and the other woman was pregnant. Him and I broke up and a month later I found out I was pregnant too. He went with me to confirm the pregnancy and a week later denied that my child was his. He did not go to any appointments with me, nor even bother asking how everything was going. He was not there for her birth and I did not put him on the birth certificate. She is now almost 3 months old and there has still been no contact. I just don't want to be in court one day down the road because he suddenly wants to be a father. He also has 3 kids by another woman who he pays child support for but never sees them. And another daughter born just weeks before mine. I will never ask him for anything and I just want to be sure if he comes around he can not take my little girl.