I want to get custody and/or joint custody of my child who is living with his mother and her husband

If the child was born after they married the husband is presumed to be the legal father.

JAMES JOHNSON, Appellant, v. KARI RUBY, n/k/a KARI POST, Appellee.
CASE NO. 4D99-4389COURT OF APPEAL OF FLORIDA, FOURTH DISTRICT
771 So. 2d 1275; 2000 Fla. App
OPINION
James Johnson (Johnson) appeals the order dismissing his Petition to Establish Paternity, Child Custody, and Child Support. We affirm.
...
Section 742.011, Florida Statutes (1999) states,

Any woman who is pregnant or has a child, any man who has reason to believe that he is the father of a child, or any child may bring proceedings in the circuit court, in chancery, to determine the paternity of the child when paternity has not been established by law or otherwise.

Johnson claims he has reason to believe he is the father of Post's child because he and Post had sexual relations around the time of conception; therefore, the court erred in dismissing the petition. The prevailing law in this state, however, is that a putative father has no right to seek to establish paternity of a child who was born into an intact marriage when the married woman and her husband object.

Were they married at the time the baby was born? Are you on the putative fathers registry for Florida?

Yes they were married I found out pretty much as we laid together the 2nd time. The mother was bringing him (my son) by for me to visit with him but these were very rare and far in between. Now there has been no contact and my son will be 1yr old in August. How should this be filed?