Legal Question in Family Law in Georgia

Plain and simple you need a lawyer. Georgia does allow service by publication if you can convince a judge you did a diligent search that failed,but frankly, about 99% of people who say they can't find a spouse find one once the judge tells them they must try harder (judges are very difficult about allowing publication with children). With a child involved you will likely not have to only show your own steps, but explain how you "know" someone tried to get married(which leaves a paper trail including an address), plus that child support enforcement searched and also did not find her. Once she is found, unless you reach an agreement,she has to be served. The court will decide custody,support and so on.

BTW,she can't be married to someone else absent a divorce. But the certified copy of that application,besides helping your case, will give you and your lawyer her address.