Richard M. Nixon's contention in his television interview with David Frost this week that he personally fired Sherman Adams, President Eisenhower's chief of staff, is disputed by several sources.

One of them, Meade Alcorn, told The Hartford Courant Thursday that he, and not Nixon, told Adams that Eisenhower wanted him to resign.

Adams, a former governor of New Hampshire, had been Eisenhower's most intimate associate until Adams was forced out over the scandal surrounding his relationship with Bernard Goldfine, a New England businessman. Adams had accepted a vicuna coat and other gifts from Goldfine, and then intervened on his behalf with several federal agencies.

Nixon told Frost that when Eisenhower decided - in September, 1958 - that Adams had to go, he "called me (Nixon) in and asked me to talk to Sherm."

"I did it," Nixon said. He told the story to illustrate how difficult it was for him to dismiss his two right-hand men, John Ehrlichman and H. R. Haldeman, in 1973.

Alcorn, the Republican national chairman at the time, said Thursday that Nixon's version "is not accurate." What happened, Alcorn said, was that Eisenhower - then on vacation in Newport, R. I. - telephoned Alcorn in Washington and asked him to tell Adams that the President wanted him to resign.

Sources close to Alcorn said that in fact, Eisenhower had suggested that Alcorn take Nixon with him for the final meeting with Adams, and that Alcorn called Nixon to make this suggestion. Nixon agreed, the sources said, but then changed his mind at the last minute, letting Alcorn do it alone.

Adams is living in New Hampshire, but could not be reached for comment yesterday.

In his memoir, "Firsthand Report," Adams wrote that no one told him he had to resign, but that Alcorn and another intermediary - not Nixon - both conveyed to him that Eisenhower was "troubled by the feeling against me among the influential supporters of the Republican Party."

In the late 1950s Nixon told his biographer, Earl Mazo, that he had two talks with Adams in which he told him his opinion that the Goldfine affair would pose problems for Republican candidates in the 1958 elections, and would impair Adams' future effectiveness. But, according to Mazo's book on Nixon, he did not say he recommended that Adams resign.

Alcorn said this week he, Alcorn, did make such a recommendation later, on Eisenhower's instructions.

His version is corroborated by a story that appeared in the Sept. 29, 1958, issue of Time magazine. According to Time, Eisenhower told Alcorn: "You've got to handle it. It's your job, the dirtiest I can give you."

Reporters who covered the White House in the Eisenhower years said yesterday that Adams and Nixon were notorious enemies at the time. Nixon denied this in his interviews with Mazo in the late 1950s.