In the fall of 1968, Donald Trump received a timely diagnosis of bone spurs in his heels that led to his medical exemption from the military during Vietnam.

For 50 years, the details of how the exemption came about, and who made the diagnosis, have remained a mystery, with Trump himself saying during the presidential campaign that he could not recall who had signed off on the medical documentation.

Now a possible explanation has emerged. It involves a foot doctor in Queens, N.Y., who rented his office from Trump’s father, Fred Trump, and a suggestion that the diagnosis was granted as a courtesy to the elder Trump.

The podiatrist, Dr. Larry Braunstein, died in 2007. But his daughters say their father often told the story of coming to the aid of a young Trump during the Vietnam War as a favor to his father.

“I know it was a favor,” said one daughter, Dr. Elysa Braunstein, 56, who along with her sister, Sharon Kessel, 53, shared the family’s account for the first time publicly when contacted by the New York Times.

Elysa Braunstein said the implication from her father was that Donald Trump did not have a disqualifying foot ailment.

For decades, Larry Braunstein saw patients in an office below Edgerton Apartments in Jamaica, Queens, one of dozens of buildings owned by the Trumps in the 1960s.

“What he got was access to Fred Trump,” Elysa Braunstein said. “If there was anything wrong in the building, my dad would call and Trump would take care of it immediately.”

Braunstein’s daughters said their father left no medical records with the family, and a doctor who purchased his practice said he was unaware of any documents related to Trump. Most detailed government medical records related to the draft no longer exist, according to the National Archives.

In an interview with the Times in 2016, Trump said a doctor provided “a very strong letter” about bone spurs, which he then presented to draft officials. He said he could not remember the doctor’s name. “You are talking a lot of years,” Trump said.

The White House did not make Trump available for a follow-up interview and did not respond to written questions about his service record.

In recent years, the diagnosis of bone spurs has subjected Trump to ridicule from critics, who have found it implausible that a healthy and athletic 22-year-old, on the cusp of being declared fit for service, could suddenly be felled by growths in his heels. Trump’s own shifting narrative over the years about his Vietnam-era experience has added to the suspicions.

The Times began looking into Trump’s draft record anew when an anonymous tipster suggested that a podiatrist who was a commercial tenant of Fred Trump’s had provided the medical documentation.