Many men don’t realize that if you impregnate a woman outside the bounds of marriage there is no automatic rights attached to having your name on the birth certificate of the child. Legally your name should be on the birth certificate. That doesn’t always happen. The law related to Establishment of children out of wedlock is Florida Statute 742.10 and you can view this law at http://www.leg.state.fl.us/Statutes/index.cfm?App_mode=Display_Statute&URL=0700-0799/0742/Sections/0742.10.html
If a woman is unfaithful to her husband and she is impregnated by another man, while legally married, the legal father is the husband and not the man she cheated with. The law continually evolves and this situation is very complicated. It is advisable for you to consult with an attorney if you find yourself in this situation.
The legal vehicle to establish a man as the legal father of the child, set up time sharing and set up child support is a Petition to Establish Paternity. https://www.flcourts.org/content/download/403319/3458248/983a.pdf
All fathers should register on the State of Florida punitive father registry at http://www.floridahealth.gov/certificates/certificates/birth/Putative_Father/index.html.