Greg Schneiders, the Jimmy Carter aide who lost out on a key White House appointment because of questions about his personal finances, was cleared yesterday of allegations he illegally received unemployment compensation in 1975.

He is now expected to be appointed to another White House staff position, close aides to the President-elect said.

Schneiders' attorney, John W. Karr, said he received a letter yesterday from Earl J. Silbert, U.S. attorney for the District of Columbia, which said, "We have concluded that no prosecution is warranted. We are therefore closing the matter."

Silbert's office had been investigating the possibility that the 29-year-old Schneiders had illegally collected $6,000 in unemployment benefits in 1975 while operating a restaurant management firm.

Schneiders started drawing unemployment benefits in December, 1974, after selling two unsuccessful Washington restaurants and leaving behind a string of bounced checks and bad debts. Some of the debts are still unpaid, Schneiders has acknowledged.

An FBI background check of potential Carter appointees documented his financial difficulties and the question about the unemployment payments routinely was referred to Silbert's office for investigation.

Schneiders insisted he had done nothing illegal because he drew no salary from the consulting firm he organized while drawing unemployment compensation.

Attorneys in Silbert's office interviewed Schneiders and others and examined his records before reaching the decision to close the case, according to the letter, Karr said.

Schneiders was hired by the Carter campaign in January, 1976, after impressing the candidate with his advance work in New York state.

He soon became one of Carter's closest personal aides and was expected to be named White House appointment secretary. He withdrew from consideration after the FBI report raised the unemployment payments question.

Schneiders was reported visiting in-laws in Philadelphia yesterday and could not be reached for comment.