Among the hopefuls is Graham’s sister, Darline Graham Nordone, who was appointed to serve the remainder of his term and is the incumbent among the ten candidates seeking the nomination.

Following her appointment by South Carolina Gov. Henry McMaster, Graham received an endorsement from President Donald Trump to continue her Senate run, calling her a "fabulous tribute" who would honor the legacy of her late brother.

However, Republican voters have called Graham’s potential to serve into question, noting that she had not served in politics prior to her brother's passing and that she had spent her career as a public administrator and disability advocate.

Other South Carolinian voters argue that while she made for a great caretaker of Lindsey Graham’s seat, they want the option to choose a candidate for the Republican ticket rather than have Trump select a replacement through his endorsement.

Who else is vying for the nomination?

Nine other candidates are seeking the Republican nomination this Tuesday; however, they are in stiff competition with Graham, who holds a decent lead and the status of incumbent over her opponents.

Rep. Russell Fry of South Carolina's 7th Congressional District and Rep. Ralph Norman of the 5th District are both seeking the nomination. Fry and Norman bring congressional experience to the race.

Former Gov. Mark Sanford, who previously served in the U.S. House, is attempting a political comeback. Businessman Mark Lynch, who finished second to Graham in the June primary, is also competing.

Other candidates include Duke Buckner, a 39-year-old attorney, teacher, and newspaper editor; Danny Lee Ford II, a 40-year-old farmer and business owner; Mark McBride, former mayor of Myrtle Beach; Glenda Gail Parker, a 79-year-old retired U.S. Air Force officer; and Samuel Shepard, a biomedical engineer.

Whoever wins the nomination will have a busy road ahead, as Sen. Lindsey Graham had already secured the Republican nomination. The winning candidate will have less time to campaign and make their case against Democratic nominee Annie Andrews ahead of the November election.

Polls close at 7 p.m. ET.

If no candidate receives a majority, a runoff is scheduled for August 25.