My daughter's is 4 1/2 yrs old and her father has not had any contact with her in 3 yrs. He has been in and out of jail his whole life and was recently just released from prison and is now a registered sex offender. My fiancé has took complete responsibility of my daughter and does everything for her for the past 3 yrs and now wants to adopt her as his own. I want to know what I can do to take my daughter's father's rights away from him. I know that he would never sign his rights away just to be difficult about it.

This is going to be hard, if he appears and can convince the court that he wants contact with them, he can also go for supervised visits and so on.
It will not be easy you will need an attorney for sure, but perhaps if he knows his child support stops, ( assuming you are making his life hard going after the money.