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Because your son lives in NY with you and has been living there for more than the 6 months required to establish jurisdiction over your son, you can certainly initiate a custody and visitation modification assessment in the NY court closest to your home and ask the NY court if it will assume jurisdiction over this case from the Georgia court because your child lives in NY and will spend the majority of his childhood in NY (basically you will have to have your lawyer build a convincing case to the NY judge that the NY courts should accept jurisidiction and be the "go to" court for any issues or problems between your ex and yourself).
Wow! I am shocked and find that interesting because the NY court CAN take jurisdiction if it chooses to do so. If you end up in a situation where he refuses to send your son back, you might be able to get them to look at the case at that point but it is a shame that you will have to go through something like that to get the NY courts to open their doors to your son's case.