Celina is a city in and the county seat of Clay County, Tennessee, United States. The population was 1,495 at the 2010 census. Celina was fou…Celina is a city in and the county seat of Clay County, Tennessee, United States. The population was 1,495 at the 2010 census. Celina was founded in the 19th century and named after the daughter of local pioneer entrepreneur and educator, Moses Fisk. In the late 19th century, Celina prospered as a logging town, receiving logs that had been cut in the forests to the east and floated down the Obey River. In 1878, African Americans were violently driven out of Celina.