A special primary runoff in South Carolina on Tuesday will test the power of President Trump’s endorsement and determine the political fate of a newly elevated senator. Early morning turnout appeared unusually strong for a runoff, which could bring a quick end to the congressional career of Senator Darline Graham, who filled the seat of her brother, Lindsey Graham, after his death last month.

Ms. Graham, a political novice backed by Mr. Trump, is fending off Representative Ralph Norman, a hard-line Republican supported by several GOP lawmakers in Washington. The winner will be the general-election favorite in November. Ms. Graham, 62, voted in Lexington, S.C., and joined Mr. Trump at a virtual rally Monday night. Mr. Norman, 73, voted in Rock Hill, S.C.

Runoffs in South Carolina typically draw anemic turnout, but this race appeared to upend trends. As of noon, about 125,000 voters had cast ballots, up about 25 percent from the primary two weeks ago, said Sydni Bain of the South Carolina Election Commission. Early voting saw some 64,000 ballots cast.

The race is a serious test of Mr. Trump’s influence in deep-red South Carolina, where he won by over 18 percentage points in 2024. However, two candidates he endorsed have fallen in the state recently. His super PAC, MAGA Inc., invested some $800,000 in the race. Trump described Ms. Graham as a “friend of mine” and a “great sister.”