Claiming dependents

My exwife and I have a beautiful son together that we alternate as court ordered for tax purposes. Last year, she was granted the right to move him to georgia with herself. As I was preparing my taxes, I went onto turbo tax to inquire if I could still claim him as a dependant because he had lived with me for the entire year, but not to claim him for  tax credit  or earned income credit purposes. I went onto turbotax and saw where I could do just such this thing. So I did, was I wrong for doing so and if so do I need to amend my prior years tax because of this?