Can my child's father sign over all his legal rights to my son even if he is on the birth certificate and paternity has been established? I am wanting to know because my fiancé wants to adopt my son.

After your married then go through the courts with a lawyer for the adoption process. Then your ex can sign his rights away. Until such time he can not.

One of the very few reasons a court will allow a parent to relinquish their rights is to clear the way for an adoption. But you have to qualify first. Get an attorney to advise what you need to do to qualify and to prepare the paperwork.