In SC, the mother is the presumed legal custodian of the child if the parents are not married. Whether the father is on the birth certificate or not, the father would need to have a finding of paternity by a judge and an order granting any custodial or visitation rights. Further, the custodial parent may seek support through the court, and have such support paid through the court and garnished from the payor's check.
With that said, child support and visitation are not related. If there is an order to pay support and that support is not paid, the court will not consider an argument that visitation was denied. The flip side is also true- if visitation is ordered and not allowed by the custodian, the court will not consider the defense that the visiting parent paid support.
You should contact an attorney or DSS to set up support. DSS will not handle the custody or visitation issues.
Hope that helps, and good luck.