I purchased my home 4 years ago. The property has a fence around it which is 2 feet into the neighbors property. Can a neighbor make you move a fence that was erected more than 21 years ago?

They could just remove the fence. It is on their property, which means it technically belongs to them. It is very likely that when it was originally erected it was put up by the person who's land it is on.

Most fences are installed a foot or so inside the property line of the owner.