"Son was born in state of FL where non custodial parent filed for time sharing." Does this mean there is an order from a court in Florida saying that this man is the dad and he gets certain visitation? Also were you ever married to dad and how long have you and child lived in Tennessee?
Depending on the answers to those questions and more you may have to file something in Florida to establish or modify or limit visitation, you may be able to file something in Nashville, TN to do the same or you may not have to do anything at all.
The answering of this question does NOT establish an attorney\client relationship. If you wish to hire me call me and we will talk about it, but as of now, I am NOT your attorney. My answers are intended for educational purposes only.