My son had a personal dna test done on hin and his son. By Georgia law does he need to let the mother know

If I'm reading your question correctly, it appears that your son did a DNA test via a home testing kit.  If that is the case I think that you have an argument not to turn over the results.  If the boys mother thinks that there might be some kind of health issue such that she needs DNA results for, then let her make application to the court to compel a more formal DNA test.  Her demand might be rejected if it is determined that it has no merit, or the court could compel your son to again be tested.  Either way, it's up to the court to decide this, not the mother.  To my mind, this was a test done in the privacy of the home and the results are not open to any other person.

Anyway, since this is a home kit you could argue that the results might not be accurate.  In my opinion,  if you don't want to turn over the results don't.  If there is a legal issue here the court will let you know.  Then just do as the court may ask, even if that involves taking another test.

However, since I'm not admitted in your state, you may want to speak further with a family law attorney in you area.

I am not licensed to practice in Georgia, and for a firm opinion on this question, your son should talk to a Georgia attorney who is experienced in family law.  One place you can find a lawyer like this is our website, http://attorneypages.com

If your son is paying child support, the child's mother has no less than joint legal custody, if not sole custody, and she probably has a right to this information. The strongest reason she could argue probably has to do with the child's health, because if he develops some sort of problem, his family history might matter and then the fact of whether your son is the child's biological father might make a difference.

In many states, though, if your son has been paying child support and spending time with the child as his father, for a long enough time, the genetics might not matter, as far as his rights go, if he has become the child's "psychological parent."  Most courts understand that changing parental relationships is hard on a child, no matter what the reason, and a good family court judge will always put the child's best interests first, as far as the law allows.