His son Lyman Kidder was a US Cavalry 2nd lieutenant serving in the 2nd Cavalry under George Armstrong Custer, and was killed in action in what would be dubbed the Kidder massacre. Jefferson Kidder was also the grandfather to noted lawman and Arizona Ranger Jeff Kidder.
Kidder studied law at Montpelier.
He was admitted to the bar in 1839 and practiced at Braintree and West Randolph. In 1875 he resigned, having been elected the territory's delegate to the U.S. Congress. He served from March 4, 1875 - March 4, 1879. He was an unsuccessful candidate for renomination in 1878, then was reappointed a justice of the territorial Supreme Court, where he served until his death in St. Paul.