"It is sad that the Democrats will do anything and say anything to try to win. The accusations that have been made about me are not only baseless and false, but disgusting."
But the Democrat-Gazette obtained court records from a lawsuit Beckham's family filed in Hinds County Circuit Court in Jackson, Mississippi, that challenged his dismissal from the school.
In October 2000, Beckham and two other classmates wore KKK outfits and were caught by school staff members and immediately given three days of in-school suspension, according to the court records.
Later, the school's director dismissed Beckham during his senior year, a decision upheld by the Mississippi Board of Education.
Alana Nichols, who's Black, was a junior at the school when she saw her classmates in the racist costumes and said she was "petrified".
"When I think about memories of high school, this is at the forefront, and that's unfortunate," Nichols said.
"My initial thought was, 'What's going to happen? Am I going to die? Is there going to be a rally?' "
Beckham, now 37, this week said he made "mistakes" as a teenager.
"I do sincerely apologise for any angst or grievances that I have caused anyone as a minor, as that is not the man that I am today," Beckham said.
"I continue to unequivocally denounce the KKK and any like-minded hate groups and the rumours that I am or have ever been part of the KKK are absolutely ridiculous."
- AP