Good Evening,
At some point you were granted legal physical custody of the child in a court, by a judge, is this correct?
If so than it should be safe to state that you are named on the birth certificate as the child's father, is this correct?
If you are named on the birth certificate as the child's father then it would be up to you or the mother of the child to petition the court to have the birth record revoked. Until such time as the birth mother can obtain a court order for paternity testing to support her claim then the child is still your legal child, if you are named on the birth certificate.
If you are wondering if you are the biological parent just go to the pharmacy and get a paternity test kit, just a simple swab of the cheek for both you and the child.
The court may rule the child custody change, but this could occur at anytime if you are or are not the biological father. Custody is based on many things including biological relationship to the child. If the child is not your biological child, the court will probably not rule in your favor, but they also may not rule in the mothers favor either if she is not fit to parent.