Heath Clay, a city councilman in Summerfield, N.C., left the voting booth last fall feeling that this was the most secure election he had ever voted in, partly because of a North Carolina law that requires both in-person and mail-in voters to show proof of identity.

Mr. Clay, a registered Republican, had done just that. But then someone told him troubling news: Jefferson Griffin, a Republican candidate for the State Supreme Court, was trying to nullify more than 60,000 votes in his closely contested race, which three vote counts had already shown him to have lost. And Mr. Clay’s name was on the list.

“Anyone who is trying to invalidate my personal vote as fraudulent — that’s a direct attack on the voters,” said Mr. Clay, who voted for Judge Griffin, who now sits on the North Carolina Court of Appeals. “It’s inexcusable to contest these legal ballots. He’s a sore loser. It is what it is, whether it be by one vote, 100 votes or 1,000 votes. We have spoken.”

The State Board of Elections’s final count showsJustice Allison Riggs, the Democratic incumbent in the race, to be the winner, by a margin of 734 votes out of the more than 5.5 million ballots that were cast. But Judge Griffin, the North Carolina Republican Party and conservative election deniers have embarked on an extraordinary effort to wipe away that result, and throw out tens of thousands of ballots that were submitted by mail or in early voting.

Who those specific voters favored in the election hasn’t been determined yet. But statewide, early in-person votes were evenly split between the two candidates, while mailed ballots heavily favored Justice Riggs, suggesting that if the challenged votes are thrown out, she could well lose the election.