In the State of Georgia, what legal forms do I need to file for sole custody of my daughter in which the father has no interest in being a parent to?

You can't just "file forms" to do something as serious and life-changing as terminate a parent's rights and responsibilities for his child. You need to get a lawyer. If he's not involved there's little benefit to doing this unless you are remarrying and want your new spouse to adopt your child.

Courts generally do not want to deprive any child of the resources and love of two parents. If the father is not contributing financially, they can do a lot to force his compliance, depending on the jurisdiction, from garnishing wages to suspending his driving license to putting him in jail for defaulting. If he's abusive, they can suspend his visitation while still requiring a financial contribution to the child's care. It's very complicated and you really need to talk to a lawyer in your area who specializes in family law. Most will meet with you for a free initial consultation and can tell you what they would try to do for you if they were representing you, and quote you a retainer and explain the expected process. I recommend you meet with several.

Sole custody is merely custody of your child with the other parent only having visitation.
It is part of a child custody agreement filed with family court.
What is the current agreement or court order?