NEW YORK — In 1968, at the age of 22, Donald Trump seemed the picture of health.

He stood 6 feet 2 inches with an athletic build; had played football, tennis, and squash; and was taking up golf. His medical history was unblemished, aside from a routine appendectomy when he was 10.

But after he graduated from college in spring 1968, making him eligible to be drafted and sent to Vietnam, he received a diagnosis that would change his path: bone spurs in his heels.

The diagnosis resulted in a coveted 1-Y medical deferment that fall, exempting him from service in Vietnam when the United States was undertaking huge troop deployments to Southeast Asia, inducting about 300,000 men into the military that year.

The deferment was one of five Trump received during Vietnam. The others were for education.

His experience during the era is drawing new scrutiny after the Muslim parents of a US soldier who was killed in Iraq publicly questioned whether Trump had ever sacrificed for his country. In an emotional speech at the Democratic National Convention last week, the soldier’s father, Khizr Khan, directly addressed Trump, the Republican presidential nominee, saying, “You have sacrificed nothing and no one.’’

Trump’s public statements about his draft experience sometimes conflict with his Selective Service records, and he is often hazy in recalling details.

In an interview last month, Trump said the bone spurs had been temporary — a minor malady that had not had a meaningful impact on him. He said he had visited a doctor who provided him a letter for the local draft board, which granted him the medical exemption. He could not remember the doctor’s name.

“I had a doctor that gave me a letter — a very strong letter on the heels,’’ Trump said in the interview.

Asked to provide the Times with a copy of the letter, which he had obtained as his fourth student deferment was set to expire, Trump said he would have to look for it. A spokeswoman later did not respond to repeated requests for copies of it.

The Selective Service records that remain in the National Archives — many have been discarded — do not specify what medical condition exempted Trump from military service.

The medical deferment meant Trump, who had just completed the real estate program at the Wharton School of Finance and Commerce at the University of Pennsylvania, could follow his father into the development business, which he was eager to do.

For many years, Trump, 70, has also asserted that it was ultimately the luck of a high draft lottery number — rather than the medical deferment — that kept him out of the war.

But his Selective Service records, obtained from the National Archives, suggest otherwise. Trump had been medically exempted for more than a year when the draft lottery began in December 1969, well before he received what he has described as his phenomenal draft number.

Because of his medical exemption, his lottery number would have been irrelevant, said Richard Flahavan, a spokesman for the Selective Service System, who has worked for the agency for three decades.

“He was already classified and determined not to be subject to the draft under the conditions in place at the time,’’ Flahavan said.

Trump has acknowledged feeling somewhat guilty for not serving in Vietnam and has stressed that if he had been called, he would have gone.

After his 18th birthday, in June 1964, Trump registered with the Selective Service System, as all men his age did. It was the summer after his graduation from the New York Military Academy, and Trump recalled filling out his papers with his father, Fred, at the local draft office in Queens.

The next month, Trump received the first of four education deferments as he worked his way through his undergraduate studies, first at Fordham, in the Bronx, and then as a transfer student in the real estate program at the Wharton School, in Philadelphia.

He received subsequent student deferments for his sophomore, junior, and senior years.

As Trump’s graduation neared, the fighting in Vietnam was intensifying, and many men of Trump’s age were looking for ways to avoid the war.

With his schooling behind him, there would have been little to prevent someone in Trump’s situation from being drafted, if not for the diagnosis of his bone spurs.

Many men of Trump’s age were looking for ways to avoid the war, said Charles Freehof, a draft counselor at Brooklyn College at the time, noting that getting a letter from physician was a particularly effective option.

Trump had a 1-Y classification, which was considered a temporary exemption. But in practice, only a national emergency or an official declaration of war, which the United States avoided during the fighting in Vietnam, would have resulted in his being considered for service.

Neither occurred, and Trump remained 1-Y until 1972, when his status changed to 4-F, permanently disqualifying him.

Still, Trump, in the interviews, said he believed he could have been subject to another physical exam to check on his bone spurs, had his draft number been called. “I would have had to go eventually because that was a minor medical — it was called ‘minor medical,’ ’’ he said.