On November 3, 2020, the Conservative Party won the vote for New York Assemblymember, 48th district. There was only one candidate listed on the ballot, Simcha Eichenstein. He was the nominee of the Democratic Party and the Conservative Party. It is very common in New York for minor party candidates to jointly nominate major party nominees. Eicnehstein is a Democrat.
But, the Conservative Party vote was higher in this race than the Democratic vote. Eichenstein polled 13,411 votes on the Conservative line and 12,570 on the Democratic line. This is the first time in the Conservative Party’s history that it had polled a larger vote than any other party in the same race (in any election for federal or state office), except in 1970, when its vote in the U.S. Senate race for James Buckley was higher than the vote for any other party. Buckley was a registered Republican and he won the race. Generally, the 1970 U.S. Senate election is considered a win for the Conservative Party, because its vote was higher than that for any other party. So, by the same logic, it seems that the 2020 race for Assembly, 48th district, was also a Conservative Party win.
There have been members of the U.S. House who were enrolled Conservative Party members, but no one ever listed those instances as “wins” for the Conservative Party, because in all those races, the Republican vote was substantially higher than the Conservative Party vote.
No news outlet seems to have reported that the Conservative Party vote in the 48th district was the highest of any party’s vote.