How do I get unbiological father off birth certificate

In Tennessee being on the birth certificate is actually not the same thing as being the legal father. It's sort of like being halfway there. You'd have to file an action in the juvenile court, and probably go through DNA testing to exclude him as the father. I don't know what kind of hassle he is causing you, but just being on the birth certificate doesn't give him any rights. You can just ignore him. If he is the biological father than that's all sort of different.