I am not on my daughters birth certificate. Nor does she have my last name. Her mother controls everything in her life. I am wondering what rights do I have as my daughters bilogical dad? Her mother tells me I have none. Iam in Georgia.

GO to court... and declare them... they will have a DNA test done to prove the claim... custody and visitation arrainged... as well as child support being established.

Assuming that you are the bio father, then you do have rights, but you have to get a court to affirm those rights. You have to prove you are the bio father. So you go to court, file for joint legal custody and a visitation schedule.