The bankruptcy trustee for Auto-Train Corp. plans to seek court approval today to fire Auto-Train's founder, chairman and president, Eugene Kerik Garfield, who yesterday refused a request to resign from the $125,000-a-year job.

The trustee, Murray Drabkin, announced late yesterday that he had asked for the resignations of Garfield and Richard A. Goldstein, Auto-Train's senior vice president and chief operating officer.

Goldstein submitted his resignation, Drabkin said, but Garfield refused to step down and last night issued a statement saying he would fight the trustee's effort to depose him.

Drabkin said he will go to court today and ask the federal bankruptcy judge, Roger M. Whalen, for permission to throw out the employment contracts of the two top executives.

Garfield, who is also Auto-Train's biggest stockholder, has a contract with the company guaranteeing him a salary of $125,000 through 1983; Goldstein's contract entitles him to $65,000 a year until 1982.

Saying the trustee's action was "without cause," Garfield said he would oppose Drabkin's request for the court to void his contract and "will seek to protect my rights under that contract should it be terminated."

Garfield stressed that he "has not and will not interfere with the trustee's management of the company during the reorganization" and denied reports he has refused to cooperate with Drabkin.

As the trustee overseeing the reorganization in bankruptcy of Auto-Train, Drabkin has the authority -- with court approval -- to conduct Auto-Train's business and to void any contracts signed by the corporation, including the top executives' employment agreement. Drabkin already has laid off about 75 employes.

Since he was appointed trustee three and a half weeks ago, Drabkin reportedly has had a series of disputes with Garfield over efforts to continue the operation of the railroad that carries passengers and their cars between Lorton and Sanford, Fla.

Garfield, 44, has run Auto-Train since the company was founded in 1969. He hit upon the idea of carrying passengers and their cars on the same train while an aide to the secretary of Transportation, organized a railroad, sold stock to the public and went into business just as most other lines were abandoning passenger service.

Garfield's contention that passenger trains could be run profitably held up until 1977, when the company plunged into the red and began losing more and more money.

The company filed for reorganization in bankruptcy last month after a plan to borrow funds from a Swiss bank collapsed and it was learned that both of the businessmen with whom the company had been negotiating the loan had criminal records.