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In his rise to the top of the crowded field for the Republican presidential nomination, Ben Carson has endeared himself to conservatives with his inspirational tale of emerging from a single-parent home to become an internationally renowned pediatric neurosurgeon.

But now, Mr. Carson is having to fend off increasing scrutiny about the veracity of various moments in his celebrated life story, which he has shared over the decades in numerous public statements and in books, including his widely read memoir “Gifted Hands.”

Recent news reports have raised questions about episodes he has recounted, including a gunpoint holdup he says he witnessed in the early 1980s and his own violent outbursts in his youth. And on Friday, Mr. Carson acknowledged that he had never been accepted to the prestigious United States Military Academy at West Point, despite numerous statements in his books and in public that implied that he had.

On Friday night, in a combative news conference in Florida in which he showed rare flashes of anger, Mr. Carson gave no ground and challenged the news media on its ethics and balance. In a mocking tone, he said reporters had not investigated President Obama, as a candidate in 2008, so intensely.

“Don’t lie,” Mr. Carson said, cutting off a reporter asking a question about West Point.

He predicted that the scrutiny would be a boon to his campaign, saying voters “understand that this is a witch hunt.”

“My prediction is that all of you guys trying to pile on is actually going to help me,” he said.

Mr. Carson also pledged not to let claims about him go unchecked. “What you are not going to find with me is somebody who is just going to sit back and let you be completely unfair without letting the American people know what’s going on,” he said.

Yet just a couple of hours after the news conference, another report, in The Wall Street Journal, challenged events Mr. Carson has recounted.

One of them, recalled in “Gifted Hands,” involved a psychology class he said he had attended at Yale University, called Perceptions 301. Mr. Carson described the professor’s conducting an honesty experiment on the class and wrote that he was the only one who passed, prompting The Yale Daily News to take his picture.

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But no photo identifying Mr. Carson as a student appeared in the newspaper’s archives, The Journal reported, and a Yale librarian told the newspaper that there was no psychology course by that name or class number during Mr. Carson’s years at Yale.

Even as national polls have put Mr. Carson in the lead, his opponents have been hesitant to attack him, aware that part of his appeal is his above-the-fray, bedside-manner speaking style that conveys a sense of unembellished truth. But the challenges to his life story have shaken that image and prompted Mr. Carson to rebut a growing notion that he has exaggerated his biography.

Some of his rivals for the nomination have seized on the reports. Gov. Chris Christie of New Jersey told MSNBC that Mr. Carson was “going to have to answer” questions about his past, while Donald J. Trump suggested in a Twitter post that Mr. Carson’s biography could be “total fabrication.”

Mr. Carson’s life story is a compelling one. In his own telling, he grew up poor in Detroit, raised by a single mother who had a third-grade education. He struggled in school and had a troubling temper. But as he grew to appreciate learning and became devoutly Christian, he began to focus on his goal of becoming a physician.

According to his account in “Gifted Hands,” he was offered a “full scholarship to West Point” after meeting with Gen. William C. Westmoreland, the Army chief of staff, because of his accomplishments in the R.O.T.C. in Detroit.

“I didn’t refuse the scholarship outright, but I let them know that a military career wasn’t where I saw myself going,” he wrote.

Elsewhere in “Gifted Hands,” Mr. Carson wrote that he had applied only to Yale because he could not afford the application fees for any more colleges. But over the years, he referred to his West Point invitation in a way that could make it seem like an official offer.

In a later book, “You Have a Brain,” he described how he had decided which college to attend: “I still had the scholarship offer from West Point as a result of my R.O.T.C. achievements,” he wrote.

More recently, in a Facebook post in August, he responded to a question on whether he had been offered a spot at West Point by writing that he had been “thrilled to get an offer from West Point.”

But on Friday, Politico reported that according to West Point, Mr. Carson had never been accepted.

Mr. Carson, in a telephone interview Friday, described his offer as less formal.

“I don’t remember all the specific details,” he said. “It was, you know, an informal ‘with a record like yours, we could easily get you a scholarship to West Point.’ ”

Technically, West Point does not offer scholarships; it is free.

The Politico article was published just after a CNN report questioned the accuracy of Mr. Carson’s accounts of violent outbursts in his youth, which are central to his often-told story of personal redemption through faith and hard work, one that has made him a favorite of evangelical Christian voters.

One vivid episode involved him trying to stab a classmate, who avoided injury because the blade hit his belt buckle and broke. “I had almost killed him,” Mr. Carson wrote. “I had almost killed my friend.” (He referred to his friend as Bob, but now says that this was a false name and that the intended victim was a close family member whose privacy he had been trying to shield.)

CNN interviewed nine friends, classmates and neighbors from Mr. Carson’s childhood, none of whom remembered the angry moments he has recounted. They generally described him as a quiet, bookish student.

In the interview Friday, Mr. Carson said those looking into his past should be able to obtain documentation of his transgressions from his junior high school. “I imagine the school has those kinds of records,” he said.

He also said that he had described his youthful attacks as episodes, rather than violent moments “all the time.”

Mr. Carson’s style of storytelling, both in his talks and in his writings, relies on dramatic recollections of long-ago details that are difficult, if not impossible, to decisively corroborate or debunk.

When he moved to Boston, he wrote in “You Have a Brain,” he lived in a tenement where “huge rats roamed in packs through the weeds out back.”

In a speech about the neighborhood, he recalled arresting scenes of violence. “I saw people lying in the street with bullet holes, stab wounds,” he said.

Last month, speaking about guns after a shooting at an Oregon college killed 10 people, including the gunman, Mr. Carson told a radio station that an armed robber had stuck a gun in his ribs at a Popeyes restaurant in Baltimore, and that he had told the man, “I believe you want the guy behind the counter.”

Reporters asked the Baltimore Police Department to verify the account, which dated to the 1980s.

In a Twitter message, the department wrote, “Based on the information that #BenCarson mentioned, there was not enough info to identify a police report in reference to the incident.”

The department also released a 24-page report explaining its efforts to track down a record of such an armed robbery.

Mr. Carson, though, said Friday that he would not have appeared in a police report on the episode because he had left the store when he could.

“I was there to buy some French fries for me and my wife,” he said. “And, you know, I was very happy to just leave.”

At an event Friday in West Palm Beach, Fla., shortly before his news conference, he was dismissive of the recent reports.

He said, “Now some left-wing organization is going to say that I can’t read, or, ‘He didn’t go to medical school!’ ”

Ben Carson Turns Heat on Reporters in Feisty News Conference In a mocking and unexpectedly theatrical appearance, Mr. Carson delivered a public scolding of the news media that has begun to question his celebrated biography.

Michael Barbaro, Nick Madigan and Dave Phillips contributed reporting.