Ex-Speaker James Watson, a State Senator until the previous session, was the candidate of the Federalist Party.
First Judge of the Albany County Court John Tayler was the candidate of the Democratic-Republican Party.
Result
Watson was the choice of both the State Senate and the State Assembly, and was declared elected.
August 1798 United States Senator special election result
Watson took his seat on December 11, 1798, but resigned on March 19, 1800, after his appointment as Naval Officer of the Port of New York. The State Legislature held a special election in April 1800, and elected Gouverneur Morris to fill the vacancy.
Election result at Tufts University Library project "A New Nation Votes" (omits part of the text, it should read: "...James Watson [of New York City, 30 votes; John Tayler,] esq. of Albany 9 - Maj. 21")