Hi and welcome to JA. Ray here to help you today.
You would have to file suit to quiet title to claim such an easement or the property itself by adverse possession.You have to decide if you can resolve it with neighbor, file such a suit, or move the fence.Honestly if you cannot resolve it with neighbor by easement it may be cheaper and faster to move the fence to comply with the property line.
You may well have a valid claim here to assert, but it has to be done through the courts , the court has to award you an order grating you the easement or possibly title to the disputed area.Again you may not want to hear this, please don't shoot the messenger here but you either resolve it or move it if you want a quick sale.A lawsuit here to quiet title involves legal fees and time even if you prevail, it would affect and possibly hold up a sale.It amounts to encroachment, such an easement without an order would not be recognized by a title company.
You make the choice here, resolve it with neighbor, move it , or file suit to quiet title claiming the property here.These are your choices under Georgia law.
I appreciate the chance to help you today.Please let me know if you have more followup.Thanks again.