In March 1815, Jonathan Fisk (DR), who'd been re-elected to New York's 6th district, resigned to accept an appointment as United States Attorney for the Southern District of New York. A special election was held in April of that year to fill the vacancy left by his resignation.
Election results
Wilkin took his seat at the start of the 14th Congress.
References
New York's 6th congressional district special election, 1815 Wikipedia(Text) CC BY-SA