Property Border

I placed a 6' cedar fence on the back yard property in NY state, but I did not place the fence on the property line border, because there is a hill and I did not want the childern playing in this area, so I placed it 15 feet before the end of the property line, Can my neighbor
in the back claim that piece of property after a certain amount of years? should I
place another fence on real border?

As a practical matter get a notarized statement from him that he recognizes it and agrees to it, and has no claim to the land. Stake it out also. But that's enough unless you want a belt and suspenders.