A classic regional battle is taking shape in Congress over a few paragraphs in the U.S. code that govern distribution of billions of dollars a year under the largest of the federal aid-to-education programs.

Ironically, the South, mainly responsible for writing the formula in 1974, is challenging the existing distribution formula.

The program, formerly known as Title I, for Title I of the Elementary and Secondary Education Act of 1965, was one of President Johnson's proudest achievements. Now it is called Chapter I.

In the 1983-84 academic year, about $2.66 billion in Chapter I funds will go to the nation's school districts for so-called compensatory education for disadvantaged children--to help them catch up. The problem is how to make sure that districts with the most such children receive the most money.

In 1974, southern legislators thought the best method was to distribute funds mainly according to numbers of children living below the official federal poverty line, as counted in the 1970 census. Disproportionate numbers of such children lived in southern states.

"What we ought to be looking at is where the poor children are," said Sen. Lloyd Bentsen (D-Tex.), who supported using the poverty line.

In the 1980 census, however, the South no longer had a disproportionate share of children in poverty, so its legislators want to shift to a new standard of distribution, giving more weight to per capita income.

Under this formula, the lower a state's per capita income the greater its share of Chapter I funds. To connoisseurs of formula fights on the Hill, it is no surprise that per capita income in the South is the nation's lowest.

If the South no longer has as many of the very poor, the region still is less well off on average than other parts of the country.

Formula fights are zero-sum games in that, whatever one area wins, another loses. In this case, the losers would include large states in the West and North, including New York and California.

Southerners hope they can tack their proposed formula onto another education bill on the Senate floor in this session, then get House Education and Labor Committee Chairman Carl D. Perkins (D-Ky.) to accept it in conference. Aides said Perkins has not been approached about it.

In a textbook example of political formula-writing using computers at North Carolina's Research Triangle, southerners have devised a formula benefiting 32 states, including almost the entire South and some in the West and North. Theoretically, that would give them 64 Senate votes.

Ellis Bateman, director of budget services and federal relations for the Georgia Department of Education, said that southern strategists are checking several other formulas with the same general impact but that "this to us seems most equitable."

Likely losers under that formula are resisting. Miriam Kazanjian, representing the New York state education department here, and Greg Humphrey, legislative director of the American Federation of Teachers, said they would rather see this year's main education bills, including one to increase the number of math and science teachers, killed than let them become the vehicle for such a rider.

"Every time there is a census result they don't like, they try changing the law," Humphrey said.

Basically, the 1974 formula takes the number of children under the poverty line in a state, as measured in the 1970 census, and gives the state a grant for each child. The grant is equal to 40 percent of the state's average outlay per pupil with some upper and lower limits. The 1970 census totals are to be replaced this fall by 1980 census figures.

Because of the South's widely heralded economic revival in recent years, the number of poor children in most states there plummeted. The 1980 census showed, for example, that in Alabama the number of poverty children age 5 to 17 dropped from 272,146 in 1970 to 195,917, or a 28 percent decrease.

In Arkansas, the number fell 29.4 percent; in Georgia, 16 percent; in Kentucky, 21.5 percent; in Louisiana, 29 percent; in the Carolinas, 30 percent, and in Mississippi, 32.5 percent. Numbers in other regions also dropped but generally not as much.

"Virtually all the southern states would lose from the use under the 1974 formula of the 1980 census," said John Wilson, executive director of the Southern Governors Association.

So Bateman and other southern spokesmen went to the computers and produced a proposal to calculate where a state's per capita income stands in relation to the national average. Then, within certain limits, they would increase its Chapter I allocation if it is below the national average and decrease it if above.

Of the 13 Southern states, only Texas has a per capita income above the national average. A few northern states that are rural or, like Pennsylvania and Ohio, suffer from high unemployment, and several Plains and western states also are below the national average.

Faring worse would be most major industrial states, with higher per capita income, such as New York, California, Michigan, New Jersey, Massachusetts, Illinois, Connecticut and Minnesota. Maryland and the District of Columbia also would lose funds.

Bateman, Wilson and others argue that the proposed formula is not just a grab for extra cash.

Part of the existing formula, they said, depends on a state's per capita expenditure for schoolchildren. The higher that expenditure, the more Chapter I aid. Most northern states have higher per-pupil expenditures because, Bateman and others said, most northern states can afford to tax and spend more.

The existing formula, they said, penalizes poorer states simply because they cannot afford to spend more per child on education. Use of the new per capita income factor in the formula would help rectify this and be fairer, they said.

But Kazanjian and education officials in several states, including Maryland, said in a memo that per capita income is not a measure of fiscal capacity at a time when the South is growing and the North fading economically.

Moreover, Kazanjian said, educational costs in northern states are higher--as are costs of living generally--so those states need a higher subsidy per poverty child.

Finally, she said, "This is not a program to redistribute income. This is a program to help the education of poor children."

Sen. Jeremiah Denton (R-Ala.) has raised the proposed change in the Labor and Human Resources Committee and said in an interview that he may offer a floor amendment to a major education bill. Other southern senators, including Sen. Dale Bumpers (D-Ark.), are said to be looking at the same possibility.

Sen. Robert T. Stafford (R-Vt.), chairman of the Senate education, arts and humanities subcommittee, said in an interview that he will oppose any floor amendment, despite the fact that his state would benefit substantially from the southerners' formula.

"This is no time to be changing one of the major programs in our educational configuration without extensive study and debate," he said.

Sen. Claiborne Pell (D-R.I.), the subcommittee's senior Democrat whose state would benefit slightly, feels the same way, aides said.