Can I get custody of my son in the state of
Gaorgia if he lives with me and his father lives in New Mexico and his father has full custody of my son

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

Second, there is no way for us to answer this question. We would need to know the circumstances of why the father has custody yet the son lives with you.