A mid-decade census was taken by New York State every ten years for the period 1825-1875, then again in the years 1892, 1905, 1915, and 1925. However, not all of the schedules survive for each county and each census year.
Contents of the New York State Census
It is well known that the New York State censuses often contain data not found in the Federal census schedules or not found in the Federal census until many years later.