FamilySearch has an index to the 1855 New York State census to their vast collection of records.
The 1855 census was the first State census that listed every name of the people in a family. Plus it also asks the relationship of each individual to the head of household. Also if a person was born in New York State then they were asked in what NY County they were born. Another question asked in the 1855 census is how long you lived in this town. This census is very helpful for NY State families.
FamilySearch says that the 1855 census isn’t complete. That is because these census records were the property of each county and over the years some of the records were lost or destroyed.. I had to do some digging to find out what counties are missing. It turns out that these counties are not in the 1855 index: Bronx, Clinton, Dutchess, Genesee, Hamilton, Nasssau, Putnam, Queens, St. Lawrence, Seneca, Suffolk, Tompkins, Westchester and Wyoming Counties.
This link will take to the search page for the 1855 New York census.