Though Mr. Lucas said in an interview that he was later told that he was in fact on the voter rolls and had been turned away by mistake, he said the situation was illustrative of larger problems, namely how hard it can be to vote in America.

Mr. Lucas, a Democrat who began his term in 2019, said he had used a utility bill to verify his identity, but during a 10-minute exchange with a poll worker, he was repeatedly told he could not be found on the voter rolls.

“I was probably a bit frustrated,” he said. “The other thing that got in my head was it’s a little embarrassing being turned away at the polls.”

Less than an hour after he tried to vote, he received a call from an election official informing him that the poll worker had simply entered his name incorrectly, inputting his last name as his first name and vice versa.

Mr. Lucas noted that his longtime polling place — where he has previously voted for himself — was a Baptist church in an area where he estimated the electorate was about 80 percent African-American.