Persia, NY is a hamlet Cattaraugus County southeast of Dayton. It was a stop on the Erie Railroad‘s line between Binghamton and Dunkirk.
The only information I have is one Erie Railroad map showing a small depot on the north side of the tracks just to the east of the point where the tracks crossed Persia Road. It was likely a short-lived station as it does not appear on timetables from 1891 onwards.
Cover: Map showing the location of Persia, NY on the Erie Railroad’s line between Salamanca and Dayton (green). The Erie’s Buffalo and Southwestern Branch (red) can be seen entering Dayton from the southwest. Author’s illustration from a 1923 topographic map.