Barnard is a city in Lincoln County, Kansas, United States. As of the 2020 census, the population of the city was 64. Barnard was first settled in …Barnard is a city in Lincoln County, Kansas, United States. As of the 2020 census, the population of the city was 64. Barnard was first settled in 1888 when a rail line of the Chicago, Kansas & Western Railroad Company reached the town, and it was incorporated as a city in 1904. Barnard was named for J.F. Barnard, a railroad employee.