The United States took federal census records other than those counting the population. These non-population census schedules that mention individual names include the following schedules for the following years:
- Agricultural: 1850-1880
- Defective,Dependent, and Delinquent: 1880
- Industrial: 1850-1870
- Manufactures: 1820, 1850-1880
- Mortality: 1850-1880
Most were not retained by the federal government and were given to state agencies willing to maintain them. Some have been microfilmed, some are available online, and some are only available in their original paper format. Your search should begin with the state archives for the state where the person of interest lived.