A descendant of President Jefferson, John H. Works Jr., is digging into America’s oldest and most delicate paternity case. By exhuming one of the president’s nephews, John Jefferson, Mr. Works hopes to settle which Jefferson is responsible for fathering Easton Hemmings by the enslaved woman, Sally Hemmings.

The Thomas Jefferson Foundation has considered Easton’s lineage a “settled historical matter” since a 1998 article in Nature, “Jefferson Fathered Slave’s Last Child,” seemed to leave no room for doubt. The theory that the president’s brother, Randolph — or his son, John — might have contributed the Jefferson DNA was dismissed.

The researchers weren’t as certain as Nature’s headline made them sound. They later clarified that other “men of Randolph Jefferson’s family” could have fathered Easton. Regardless, the Hemmings were confirmed as branches of the president’s tree and welcomed at Monticello, the president’s home in Virginia.

At issue is who contributed the Y chromosome that the Hemmings descendants share with the Jeffersons. The Y is passed down through men and the president’s only son with his wife, Martha — Sally’s half-sister — died in childhood. With no direct male line to test, researchers relied on Randolph’s.

The petition to exhume John from Nashville City Cemetery and test him against Easton’s descendants was filed in court on November 19. Another Hemmings child, Madison, has no verified male line of descendants; his paternity also remains an open question.

The allegations about Jefferson were first published in 1802 by a notorious journalist, James T. Callender, who denigrated Sally Hemmings as the Jefferson’s “concubine.” He’d helped pillory the president’s foes but, after a falling out, sought revenge.

Details of “the Randolph Jefferson DNA Study” were provided by Mr. Works to The New York Sun. Its “goal” is to “generate scientifically sound data that has never before been available.” Their petition for exhumation says that the “samples” from John’s remains will “shed new light on a matter of great historical importance.”

The study seeks to collect “authenticated Y-chromosome DNA from a known Randolph Jefferson male line.” They’ll compare it to the DNA used in the Nature study and, “for the first time, directly test whether Easton Hemings’s lineage matches” Randolph’s line.

Science is meant to be a dispassionate pursuit of facts. Yet history, like that surrounding slavery, can open old wounds. Before 1870, African-Americans were not even recorded by name in the United States Federal Census, resulting in a barrier to tracing ancestry that genealogists refer to as the “Wall.”

Oral traditions were all that enslaved persons had to remember their history. The Hemmings descendants bristled that they were denied their birthright because the word of a black woman held in bondage was rejected in favor of the author of the Declaration of Independence.

“We are fully aware,” the study’s statement said, “of the sensitivity surrounding this question. The parentage of Sally Hemings’s children has been debated for over two centuries, and public reaction can be emotional and polarized.” To many, it will be once again calling the enslaved woman a liar.

The delicacy recalls another White House paternity case. President Harding’s mistress, Nan Britton, alleged in her 1927 book, “The President’s Daughter,” that the chief executive — who passed away in 1923 — had fathered her child, Elizabeth.

In the book, Britton rejected the term “illegitimate” and advocated for the right of women to name the fathers of children like Elizabeth on birth certificates. She cited “the need for legal and social recognition and protection of all children in these United States born out of wedlock,” resulting in changes to laws in that direction.

The Hardings denied Britton’s assertions, believing the president had been sterile. Yet his grandnephew, Peter Harding, tested with Elizaeth’s son, James Blaesing in 2015. There was a 99.9 percent DNA match. Britton, who died in 1991, ten years after her daughter, had been telling the truth about the man she remained devoted to her entire life.

DNA technology provided clarity to Harding’s record and can do the same for Jefferson’s. “The purpose of this work,” the statement from Mr. Works said, “is not to reopen old conflicts, but to bring the best available science … to bear on one of the most significant unresolved questions in early American history.”