Brother of Myer Moses II and uncle of Isaac Harby, Isaac Clifton Moses was a founder of the Reformed Society of Israelites. Isaac Moses and his wife Hannah Lazarus had 12 children. One daughter married the artist Theodore Sidney Moïse, another wed reform leader Abraham Moïse, Jr. In 1819, Moses was listed in the Charleston directory as a justice of the peace; in 1820, he entered a legal partnership with Christian Staley. While vacationing with his wife in Branford, Connecticut, they were thrown from a buggy and he was killed. Hannah returned home to Charleston but died within a year of her injuries.