A special election was held in New Hampshire's at-large congressional district on November 18, 1799 to replace a vacancy caused by Peleg Sprague (F) declining to serve in the 6th Congress.
Election result
Sheafe took his seat with the rest of the 6th Congress when the 1st session began on December 2, 1799
References
New Hampshire's at-large congressional district special election, 1799 Wikipedia(Text) CC BY-SA