The release of an audit showing a $68.3 million surplus for the D.C. government has dampened the City Council's ardor for restraining spending next year and sent special interest groups clamoring for a share of extra funds that Mayor Barry's aides insisted yesterday only exist on paper.

City Administrator Elijah B. Rogers said the surplus revenues reported for fiscal 1981 already have been used to pay off part of the city's accumulated debt, including $33 million in court-ordered tax refunds to nonresident professionals and $35 million in current and overdue bills.

Nonetheless, the audit report spurred speculation that the city was far better off financially than Barry had let on last year when he cut numerous city programs and eliminated hundreds of jobs from the city work force, and suggested that it was possible the city could spend more next year than the mayor has proposed.

In the wake of the audit, City Council Chairman Arrington Dixon is overhauling his proposal to reduce Barry's fiscal 1983 budget proposal by 3 percent in selected agencies in order to provide an additional $16.3 million to city schools.

Dixon's new plan, expected to be released today, would still provide extra money for the schools while eliminating about half the cuts he originally proposed, according to an aide. Dixon said he is counting on stronger than projected revenues--a major contributor to the $68.3 million surplus--and accounting adjustments to the city's long-term debts to make up most of the difference.

A coalition of about 40 community and social service agencies protested this week that Barry's proposed budget for the D.C. Department of Human Services is underfunded.

Cheryl Fish, a spokeswoman for the Community Coalition on Financial Accountability, said that some members of her group wondered why there wasn't extra money for Medicaid and Aid to Families with Dependent Children (AFDC) in light of the city's improved financial situation reflected in the audit.

Meanwhile, representatives of Parents United for Full Funding, which lobbies for more aid for public schools, buttonholed council members after the audit was released Monday, hoping to get a cut of what they saw as a massive pot of surplus funds.

Council members, who have accused Barry of playing tricks with the city's spending and revenue projections, are reluctantly following the mayor's line in explaining to constituents why none of the surplus is available for future spending.

Moreover, some of the members who only a few short weeks ago were complaining that the mayor had been overly optimistic in making revenue projections for fiscal 1983 now are saying that there may be a lot more available in tax revenues than even the mayor is letting on.

These council members complain that Barry has refused to give them enough data to make informed judgments about his budgets and that the audit was the only sound information they have received in months.

Dixon and council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, said yesterday that they each would develop their own revenue projections using the city's computerized financial management system.

"One of the biggest problems in this government is the stepchild nature of the way the council is treated," Wilson said.