No the abandonment law you are referring to is only applicable when the state is making a determination as whether both parents parental rights should be terminated and the child is made a ward of the state. You will not be able to terminate the fathers rights and responsibilities unless and until there is another person willing to adopt the child , usually a stepparent.
Daniel Bachert, Esq.
The Bachert Law Firm, P.A.
330 Clematis Street, Suite 222
West Palm Beach, Florida 33401
Please be aware and advised that this public forum is designed to provide only general information, to give you a basis of legal knowledge. This public forum does not give you attorney-client privilege. You and I have not entered into an attorney-client relationship. I am not responsible for your legal rights and this answer is based solely on the information you have provided in your question and as always, I would advise that you arrange for an in person consultation with an attorney from my firm or another Family Law attorney familiar with Florida Family Law who can analyze the specific facts and circumstances of your case more closely to better advise you.
Sign up to receive a 5-part series of useful information and advice about child custody law.