The ranking Republican on the House Appropriations subcommittee on the District chastised Mayor Marion Barry yesterday for what he said were "corruption and mismanagement which seem to be growing problems in the city."

Rep. Lawrence Coughlin (R-Pa.), questioning the mayor during a hearing on the District's fiscal 1987 budget, recited a list of widely publicized corruption cases linked to Barry's administration and asserted that "too many people are not doing their jobs . . . or are giving the appearance of illegal gains."

Rep. Frank R. Wolf (R-Va.), noting several other controversial actions by city employes, declared that the District's support in Congress is "beginning to erode."

"I think the District is losing support on Capitol Hill," said Wolf, who threatened to seek cuts in the federal payment to the District if the mayor and D.C. City Council Chairman David A. Clarke do not work to raise the legal drinking age in the District from 18 to 21.

Barry parried Coughlin's charges, asserting that the "actions of a few" should not reflect on the "99.9 percent" of honest D.C. employes, and also disputed Wolf's contention that the city's support was declining in Congress.

"I see just the reverse," Barry said, alluding to what he termed substantial support in Congress for the city's budget legislation last year.

In other developments at the hearing:Subcommittee Chairman Julian C. Dixon (D-Calif.) said he supports the payment of $20 million in federal funds in fiscal 1987 for the construction of a new prison in the District, noting that the money should be in addition to the projected $445 million federal payment to the District. The Reagan administration has favored including the funds in the federal payment, which would mean a net loss to the city of $20 million. Barry cited a study that recommends expansion of the Washington Convention Center to remain competitive with larger facilities such as the Jacob K. Javits Convention Center, which opened in New York City in April. The mayor disclosed that the city's fiscal 1986 revenues are $40 million higher than projections and that supplemental budget requests this year likely will be targeted to cover rising costs in the city's overcrowded prison system as well as a legislated pay increase for D.C. police. Barry, citing a $16.8 million cut in fiscal 1986 federal funds due to the Gramm-Rudman-Hollings budget cutting act, said it was possible the city might not be able to reduce its accumulated general fund deficit as much as had been promised.

Coughlin's lengthy narrative of corruption cases followed more friendly questioning from Democrat Dixon and referred to the conviction of former deputy mayor Ivanhoe Donaldson and the resignation of former deputy mayor Alphonse G. Hill, who acknowledged receiving $3,000 in cash payments from a city contractor, as well as cases involving at least seven other city employes.

Rep. S. William Green (R-N.Y.) joined the questioning, asking Barry and Clarke whether the city ought to step up its internal investigative powers. Clarke said his proposed Municipal Integrity Act would provide such powers and Barry said existing agencies, which he said had been responsible in the past for uncovering wrongdoing, were adequate.

Wolf and Coughlin were highly critical of a memo written by Richard Clark, a congressional liaison for the City Council, who advised council members on ways to pressure Sen. Arlen Specter (R-Pa.), chairman of the Senate Appropriations subcommittee on the District, to end his insistence on new prison construction in the District.

Clarke, noting that he was no relation of Richard Clark, apologized to Coughlin for the memo and said he had attempted to reach Specter to make an apology. Later in the hearing, Clarke bitterly protested Wolf's criticisms, saying "you can take back" home rule if the city's great strides in self-government are going to be submerged in criticisms from Congress.