As a teenager growing up in rural Sumter County, Brian Benenhaley resented the white people who looked down on his dark-skinned father. The resentment fueled his ambition, and he took a certain satisfaction, on high school awards nights, in bringing his father the trophies and plaques he had won.

“I’d give them to my dad, and watch some of the white folk have to come by and acknowledge that your boy did O.K., or maybe even a little better than O.K.,” said Mr. Benenhaley, 44, who is now a corporate lawyer based in Columbia, the state capital.

Such stories of pride and prejudice are common among nonwhite people in the Deep South. But Mr. Benenhaley belongs to an uncommon tranche of the population, one that never fell neatly into the region’s old racial binary.

Based on little more than oral tradition, they call themselves Turks, and have long claimed to be a kind of “white folk” themselves; indeed, they have been known to harbor their own prejudices. Mr. Benenhaley said his father, who died in 2013, would have been scandalized if his sister had dated a black boy....

In recent years, even some of the Turks have come to doubt their origin story, choosing instead to embrace the idea that they are Native American. In 2013, the South Carolina government recognized some of them as the Sumter Tribe of Cheraw Indians, a step that opened a rift in the small community.

Mr. Benenhaley brushes aside that idea. “We never lived as American Indians,” he said.

Now there is another layer of both clarity and complication: A new book, published by the University of South Carolina Press this spring, argues that the Turks’ quasi-mythic patriarch was not a myth at all, but a real man who probably hailed from the Middle East, or somewhere close to it.