By voting recently to cut the federal payment to the District of Columbia, a congressional panel has revived a continuing dispute that has marked financial relationships between the nation and its capital city for at least 143 years.

Ever since a committee headed by Sen. Samule L. Southard (Whig N.J.) recommended in 1835 that the U.S. government pay 40 percent of the District budget, officials have searched for a formula that is fair to both the city and to federal taxpayers.

The federal payment of $264 million recently recommended by Rep. William H. Natcher (D-Ky.) and his House D.C. Appropriations Subcommittee would be about 25 percent of the city's proposed operating budget of nearly $1.3 billion for the 1979 fiscal year.

That proposed payment is $12 million below the payment for 1978 and $53 million under what President Carter has recommended.

If the subcommittee recommendations become law, existing municipal programs would be maintained at about their present levels, but there would be no new programs added, including one that calls for civilian enforcement of city parking laws.

The full House Appropriations Committee will consider the proposals next Thursday after Congress returns from its holiday recess. After that, the budget and payment will be considered by the full House and the Senate.

Although city officials were stunned by the cut voted by the subcommittee last month, official reaction has been muted.

The city home rule charter, which went into effect in 1975, left ultimate control of the city budget and the federal payment in the hands of Congress. City Council members and other officials have said the latest congressional action reaffirms the need for local budget autonomy.

The charter authorizes, but does not require, Congress to appropriate a federal payment of $300 million. Legislation supported by the White House to raise that ceiling to $317 million has not been passed by either chamber of Congress.

In theory, the federal payment is designed to compensate for services the city provides to government installations and to make up for the tax revenues the city cannot collect on government-owned land and foreign embassies. Of usable city land, 53 percent is tax-exempt. Moreover, 57 percent of the wages earned in the District go to suburbanites, and cannot be taxed by the city.

In practice, Congress has used the federal payment as a way of balancing the city budget by appropriating enough to make up the difference between the city's tax income and its budgeted expenses.

Because expenses rise year by year, the payment usually rises, too. Only twice since World War II - 1951 and again in 1956 - has Congress trimmed the payment below the previous year's level as it is proposing now.

Mayor Walter E. Washington, stating the city's official position, has called upon Congress to switch to a method under which the city could predict the amount of each year's payment, and prepare a budget to keep within that amount.

In a touch of historic irony, the mayor has urged Congress to authorize on a continuing basis, a formula based on the 40 percent payment urged by Sen. Southard in 1835 but not adopted.

Instead of paying a straight 40 percent of the budget, however, the mayor wants the U.S. Treasury to pay an amount equal to 40 percent of what the city raises in locally levied taxes.

In another historic parallel, City Council member Marion Barry has proposed a resolution asking the federal government to finance half the city budget. An act of Congress that included just such a 50 percent formula was signed into law 100 years ago by President Rutherford B. Hayes, and it remained in effect until 1920.

Since then, the federal payment has ranged from a high of 43 percent in 1921 to a low of 8.5 percent in 1954. It has averaged about 25 percent for the past five years.

As the total size of the city budget has risen sharply this past decade, the dollar amount of the federal payment has gone upward, too - but not as fast as inflation, city officials contend.

One figure shows dramatically how fast costs have rise. The total D.C. budget as recently as 1965 ($265 million) was not as large as the federal payment alone is in 1978 ($276 million).

Michael Bell, in a paper written last year for the D.C. Tax Revision Commission acknowledged the complexities of coming up with a system that protects both sides. For example, he said that setting the dollar amount of the federal payment in advance could encourage increased local spending.

To eliminate such a situation, he said Congress could set up a method for reviewing the city budget items separately from setting the level of the federal payment.

"The people of this District have a right to protest being left subject to the whim and caprice of Congress with each recurring session." observed one lawmaker as he grappled with the problem. The lawmaker was Rep. Joseph C.S. Blackburn (D-Ky.) and he made that comment on May 7, 1878.