If my child was given to the perssumed father and he is suppose to have custody and joint legal yet he lmoved from san diego to flordia where she was taken to and the case started in san diego. But yet his mother has her in her home and I just moved out to flordia to be closer to my child and have her with her siblings and I have a place and good job can I fight for custody to be given back to me since she doesn't live with him and his mom has her and makes it hard for me to be close with her at times. What can I do to fix this

Sue for custody and/or visitation in Florida - that's apparently where you, the father and the child live.

The Court awarded custody to a person who was not tested and proven to be the father?

Did you have visitation on San Diego? Did the father have court permission to move? Why was he awarded custody and not you? Do you have a visitation order now?

So if his mother has the child living in her home though the father has the papers saying he has custody and I want her to live with me what can I do...

It doesn't matter who the child is living with. You go to court and file to regain custody. You can use the fact (if you can prove it) that the child is living with her grandmother to regain custody.