My neighbor joined her fence to mine, which is on MY property...

I was the first to have a fence built, entirely on my property. The fence company made sure they dug the holes for the fence posts at least 6 inches (more like 8 or 9) INSIDE the property lines on BOTH sides. The neighbors on one side later "added to" my fence and voluntarily paid me for half the cost of the side of fence that we now share. But even after telling me they would pay, the neighbors on the OTHER side are REFUSING to pay for half of the fence we now share since THEY also built a fence to attach to my fence. Since my fence is completely on my property, both new fences (coming from each side of me) cross over the property line and physically attach to my existing fence. One of the neighbors acknowledges that they are indeed benefitting from our shared side, yet the other neighbor has written me a nasty note admonishing me for daring to even ASK that they pay for half of the fence line we share. These two neighbors are like NIGHT and DAY when it comes to friendliness and consideration, obviously. The latter neighbor's note was extremely hostile towards me even though have built a fence that is ON my property and physically attached to MY fence, which I will always take responsibility for in maintaining.

Please, someone, give me any advice on how to find ANY legal basis in GEORGIA to make sure they pay me for crossing onto my property with their fence, even though it's only a foot or so...

Thanks!