property line dispute

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my grandparents owned a piece of property and was purchased in the 60's. the property was agricultural and is now ag/commercial. when they passed away, my parents received the property. the property next to us has been an empty field the entire time. we had to replace fence (but put it in the exact same place as previous fence) in 2001 due to fire in neighboring field. owner of field has now sold property and new owner is saying the fence is on his property and would have to move it 4 feet in which would put the fence literally at the exact spot of the structure which has been there since the 60's. we have offered to buy the 4 feet of property that runs behind the structure but new owner refuses. my mother read an article about something similiar where a neighbor actually put in a sidewalk and it was partly on the neighbors property. the neighbor never complained until quite a few years later and had obviously seen the construction and the sidewalk for many years. i believe they called it adverse possession. does anyone have any suggestions on my situation.