Look at my AVVO Legal Guide on interstate custody cases. You need to get a custody order in NY, and register it in FL. For more details you schedule a brief paid consultation with an attorney who is familiar with the UCCJEA.
DISCLAIMER: This AVVO Answer is provided for general educational purposes only. By using or participating in this site you agree and understand that there is no attorney client relationship between you and the attorney responding, and no attorney-client confidentiality. The law changes frequently, and varies from jurisdiction to jurisdiction. The information provided in this Answer is general in nature and may not apply to the factual circumstances described in your question. The applicable law and the appropriate answer may be different in the State or States where the relevant facts occurred. For a definitive answer you should seek legal advice from an attorney who (1) is licensed to practice in the state which has jurisdiction; (2) has experience in the area of law you are asking about, and (3) has been retained as your attorney for representation or consultation. Your question and the attorney’s answer may be used for promotional or educational purposes.
if you have previously acknowledged paternity and you have an order of filiation you can file in the appropriate county in New York where your son lives with his mother a custody/visitation proceeding or alternatively if a Court order exists you may want to pursue a Writ of Habeus Corpus proceeding.