Babygurl is correct on this one.
He doesn't have to voluntarily claim anything. You can make the court force him to take a DNA test. After paternity is established, a child support order can be placed and enforced.
First he has to be officially be declared the father. He can do it the easy or the hard way. Then the court will determine what amount he'll be forced to pay, up to a maximum of 28% for 1 child if I remember correctly.
Found this on a quick search of GA divorce law FAQ:
"Is a father who never married the mother still required to pay child support?
The short answer to this question is yes. When a mother is not married, however, it's not always clear who the father is. An "acknowledged father" is any biological father of a child born to unmarried parents for whom paternity has been established by either the admission of the father or the agreement of the parents. Acknowledged fathers are required to pay child support.
Additionally, a man who never married the child's mother may be presumed to be the father if he welcomes the child into his home and openly holds the child out as his own. In some states, the presumption of paternity is considered conclusive, which means it cannot be disproved, even with contradictory blood tests. "
Hope that helps.