On October 6, 1814, prior to the beginning of the Fourteenth Congress, Representative-elect Benjamin Pond (DR), who'd been elected to New York's 12th district, died. A special election to fill this vacancy was held in April, 1815.
Election results
Adgate took his seat at the beginning of the 14th Congress.
References
New York's 12th congressional district special election, 1815 Wikipedia(Text) CC BY-SA