I have owned and lived on present property since 1984. The adjoining landowner showed us the property lines?

at the time of purchase (we bought some land from her at that time, as well as from some others). Then, as well as as recently as yesterday, this lady and her husband told me it was my land all the way to the road. I have cared for (mowed, pruned trees, improved a driveway with gravel and red rock, grated the driveway) since I bought the property. About 18 months ago, I saw a map at the courthouse showing this lady owned 0.3 acre strip between my land and the road; I thought it was just a mapping error. When I mentioned it to her around that time, she told me I did own that land. They now want to sell their neighboring property, as well as this 0.3 acre parcel that I have always believed was mine. As recently as yesterday, they said it was mine. Now they won't sign the Quit Claim deed because their daughter says no. Can I adversely possess, and what are my chances at success? They have seen me improving the drive and caring for this strip of land all these years without comment.