If the guy I thought to be the father signs the birth certificate and then isn't the bio father does he still have rights if I leave him

Yes, he is fully and legally the father at this point. And may not even be able to be removed, depending on where you live, each state in the US is different and different countries view this differenly.

In some areas if it has went uncontested over a certain time he will remain the legal father forever, in other areas he may have the right to contest it.

It has been two years we live in Florida so how would it workout for me now?