A special election was held in New Hampshire's at-large congressional district on August 28, 1797 to fill a vacancy created by the resignation of Jeremiah Smith (F) on July 26 of the same year. Smith had been appointed United States Attorney for the District of New Hampshire.
Election results
New Hampshire electoral law required a majority for election. As no candidate won a majority on the first ballot, a run-off election was held October 30, 1797
References
New Hampshire's at-large congressional district special election, 1797 Wikipedia(Text) CC BY-SA