Late in 2015, a former Trump Tower doorman named Dino Sajudin met with a reporter from American Media, Inc., the publisher of the National Enquirer, at a McDonald’s in Pennsylvania. A few weeks earlier, Sajudin had signed a contract with A.M.I., agreeing to become a source and to accept thirty thousand dollars for exclusive rights to information he had been told: that Donald Trump, who had launched his Presidential campaign five months earlier, may have fathered a child with a former employee in the late nineteen-eighties. Sajudin declined to comment for this story. However, six current and former A.M.I. employees, who spoke on condition of anonymity because they feared legal retaliation by the company, said that Sajudin had told A.M.I. the names of the alleged mistress and child. Reporters at A.M.I. had spent weeks investigating the allegations, and Sajudin had passed a lie-detector test, during which he testified that high-level Trump employees, including Trump’s head of security, Matthew Calamari, had told him the story.

The New Yorker has uncovered no evidence that Trump fathered the child. A spokesperson for the Trump Organization denied the allegations, including the assertion that Calamari told Sajudin the story. When I reached out to the alleged daughter, she declined through a representative of her employer to answer questions. Her mother did not respond to repeated requests for comment. I spoke with the father of the family, who said that Sajudin’s claim was “completely false and ridiculous” and added that the Enquirer had put the family in a difficult situation. “I don’t understand what they had to pay this guy for,” he said. The New Yorker is not disclosing the family members’ names, out of respect for their privacy. Regardless of the veracity of Sajudin’s claims, legal experts said that A.M.I.’s payment to Sajudin is significant because it establishes the company’s pattern of buying and burying stories that could be damaging to Trump during the Presidential campaign.

Sajudin met the A.M.I. reporter at the McDonald’s that winter night to sign an amendment finalizing the transaction and adding a million-dollar penalty if the ex-doorman were to disclose the information without A.M.I.’s permission. According to a source with knowledge of the meeting, the two of them signed the amendment—an unexecuted copy of which was obtained by The New Yorker—and Sajudin remarked that it was going to be “a very merry Christmas.” Shortly after the company paid Sajudin, the chairman and C.E.O. of A.M.I., David Pecker, who has spoken publicly about his friendship with Trump, ordered the A.M.I. reporters to stop investigating, the sources told me. One of the employees involved said, “There’s no question it was done as a favor to continue to protect Trump from these potential secrets. That’s black-and-white.”

A.M.I.’s thirty-thousand-dollar payment to Sajudin appears to be the third instance of Trump associates paying to suppress embarrassing stories about the candidate during the 2016 Presidential race. In August, 2016, A.M.I. paid Karen McDougal, a former Playboy model, a hundred and fifty thousand dollars for her story about a nine-month affair with Trump, and then never published an article about it. (A.M.I. said her story was not credible.) In October, 2016, Trump’s personal attorney, Michael Cohen, paid Stephanie Clifford, an adult-film actress who performs under the name Stormy Daniels, a hundred and thirty thousand dollars to keep her account of an affair with Trump secret. (Clifford’s agreement was distinct from McDougal’s in that it was arranged directly with Cohen. A.M.I. was not party to the contracts between Cohen and Clifford that have been released.)

Two of the former A.M.I. employees said they believed that Cohen was in close contact with A.M.I. executives while the company’s reporters were looking into Sajudin’s story, as Cohen had been during other investigations related to Trump. “Cohen was kept up to date on a regular basis,” one source said. Contacted by telephone on Wednesday, Cohen said that he was not available to talk. Subsequent efforts to reach him were unsuccessful. On Monday, F.B.I. agents raided Cohen’s hotel and office. The Times reported that the agents were looking for records related to the payments to McDougal and Clifford, as well as correspondence between Cohen, Pecker, and Dylan Howard, A.M.I.’s chief content officer.

The White House declined to comment. A source close to the White House said that Trump “did not have an affair. This is a totally false accusation. And I’d refer you to A.M.I.”

Texts and e-mails from November of 2015 show that, before reporting was halted, the National Enquirer team was pursuing leads and trying to confirm Sajudin’s story. Reporters had staked out the homes of the alleged mother and daughter. The company had also hired an outside private investigator named Michael Mancuso, a former criminal investigator and the owner of Searching for the Truth Investigative Services, who administered the lie-detector test. (Mancuso declined a request for comment.) Lie-detector tests are notoriously flawed, and the test assessed only whether Sajudin had heard the story, not whether there was truth to the underlying claim.

Sharon Churcher, one of the lead A.M.I. reporters on the story, told me, “I do not believe that story was true. I believed from the beginning it was not true.” Other employees at A.M.I. had questions about Sajudin’s credibility. In 2014, a Web site registered through a service that obscures the identity of the author claimed that Sajudin had made similar accusations against a Trump Tower resident named Lawrence Penn III, and that those accusations were false. (Penn could not be reached for comment. In 2015, he pleaded guilty to securities fraud, and he is currently serving a six-year prison sentence. Penn’s lawyer did not respond to a request for comment.) When I reached out to Sajudin, he responded, in an e-mail, “My time is valuable. What’s your offer??” After being told that The New Yorker does not pay sources, Sajudin declined further requests for an interview.

Although many of the A.M.I. sources I spoke with expressed skepticism about Sajudin’s claims, all six agreed that A.M.I. made a concerted effort to shut down the story. Several said that they believed the coverup, rather than the story itself, was of public importance. One told me that, after the polygraph came back positive, “the decision was made at a high level to pay this source those funds and to put this thing to rest without an investigation taking place.” A.M.I.’s decision was unusual even in the context of the company’s other efforts to purchase stories in order to bury them, a practice known as “catch and kill.” Another source, who believed that A.M.I. suppressed the story to help Trump, said of Sajudin, “It’s unheard of to give a guy who calls A.M.I.’s tip line big bucks for information he is passing on secondhand. We didn’t pay thousands of dollars for non-stories, let alone tens of thousands. It was a highly curious and questionable situation.”

A.M.I. later attempted to prevent other outlets from reporting on the story or the company’s payout. In the summer of 2017, the Associated Press began investigating A.M.I.’s suppression of the story. At one point, reporters were hours away from posting a piece, but A.M.I. assembled a legal team to lobby against publication. The team included Lanny Davis, a crisis manager and longtime confidant of Bill and Hillary Clinton who did similar work on behalf of Harvey Weinstein. Davis and Howard met with a reporter, an editor, and a lawyer from the Associated Press. Citing attorney-client privilege, Davis said that he could not reveal the legal advice he gave Howard, but he described some of what happened in the meeting. Davis told me that Howard presented the A.P. with claims that cast doubt on Sajudin’s character, including the allegations on the anonymous Web site. “When Dylan told me he had these documents and he hoped he would kill the story, my opening statement was, ‘I am not here to kill any story. That’s not what I do for a living,’ ” Davis told me. “I encouraged my client, Mr. Howard, to reveal what he had about the source of the story.” Davis said he told the A.P., “It’s up to you to decide whether to write the story as a ‘he says, he says’ or not.” At the time, the A.P. did not run the story.

On Wednesday, thirty minutes after The New Yorker contacted A.M.I. for comment about the payment to Sajudin, Radar Online, an A.M.I. publication, posted a story acknowledging the thirty-thousand-dollar payment but saying that the former doorman’s story was false. The Radar Online piece quoted Howard saying, “When we realized we would be unable to publish, and other media outlets approached the source about his tale, we released Sajudin from the exclusivity clause that had accompanied his $30,000 payment, freeing him to tell his story to whomever he wanted.” Two A.M.I. employees told me that they’d never seen such a release during their time at the company. A.M.I. has said that Karen McDougal, the former Playboy model, has a similar amendment to her contract, but McDougal argues that the company continues to try to prevent her from talking to the press.