CaN my FiaNce Adopt My DaughTer If her biological father is not on the birth certificate?

when my daughter was born i did not put her biological father on the birth certificate. nobody signed it so it stayed blank. her father has been in and out of her life. within the last couple of months he has done nothing for her or has not even made an attempt to see her. I've decided that it is best he does not come in and out of her life anymore and its better for him to not even come around. knowing he has no custody of her or any rights cause he is not on the birth certificate i want my fiance to adopt my daughter so we can move on with our lifes and he can continue to care for her like he has been. if the biological father decides he wants to try and prevent us from doing this is there any way that they can legally make me give him a paternity test? i know if my fiance and i want to we both can sign an acknowledgement of paternity w/out a paternity test and itll be like he was her real father. can somebody give me a little more information about this situation ?