Fairfax County School Superintendent Robert R. Spillane ignited a debate between Virginia's educational haves and have-nots when he called on state lawmakers yesterday to be sympathetic to the problems of school systems in affluent areas.

Spillane, steward of one of the largest and wealthiest school systems in the nation, appealed to members of the Virginia legislature's chief spending committees, meeting in Fairfax, to compensate areas such as Northern Virginia that spend large parts of their local taxes on education and face extraordinary educational costs.

Three-quarters of the way through his speech, Spillane was interrupted by Del. Ford C. Quillen, a drawling, soft-spoken Democrat who represents an impoverished wedge of Appalachia in Virginia's southwestern corner.

"Won't we just compound these disparities that already exist {between schools in rich and poor parts of the state} . . . if we come in and spend more money for you all?" asked Quillen.

Spillane, former superintendent of the Boston schools, responded in his flat Massachusetts accent that he was "speaking specifically about the problems indigenous to Northern Virginia."

When several Northern Virginia lawmakers jumped into the discussion, it was cut short by Senate Majority Leader Hunter B. Andrews (D-Hampton), who said: "Do we need a running debate among ourselves when we're up here to be enlightened by Dr. Spillane? We can argue among ourselves downstate."

The exchange foreshadowed a gathering controversy over the appropriate role of the state in compensating for the uneven distribution of wealth and high-quality public schools in Virginia.

Wealthy localities such as Fairfax County pay about 65 percent of the cost of operating their school systems, while some poor rural areas rely on the state to pay the same proportion of school funds.

Some legislators say there is a growing perception in the General Assembly that disparities between rich and poor school systems are mounting and that it is the state's obligation to make up the gap.

The Joint Legislative Audit and Review Commission, the research arm of the General Assembly, is conducting a study of the distribution of state education funds. The findings are expected to be made public this fall, in time for the start of legislative deliberations in January on the state's 1988-89 biennial budget.

Some Northern Virginia legislators think the commission's report will conclude that wealthy localities must do more to help themselves. Such a conclusion, they say, could put Northern Virginia on the defensive in the battle among regions for education funding in the state budget.

"I think it's going to be a big problem for us," said state Sen. Clive L. DuVal 2d (D-Fairfax), head of the Northern Virginia delegation to the legislature.

In an interview, Quillen said that Southwest Virginia schools "are in a bare situation." He added: "It's the rich get richer and ther poor get poorer . . . . We can't let the children I represent continue to be at such a disadvantage. They've got a future in this country too."

In his speech, Spillane stressed that Northern Virginia's schools face a unique set of demands: the high cost of living that drives up costs and salaries; the expectations of well-educated parents; the many students for whom English is a second language, and a higher incidence of handicapped students.

He also stressed the heavy tax burden shouldered by Northern Virginia localities to pay for schools and hinted that some rural areas of the state have preferred to pay for their schools with state and federal funds rather than local property taxes.

"An equitable system of funding public schools in any state should take into consideration the extraordinary variance in local tax effort that has been typical among Virginia's school divisions," he said. He said the state should "reward rather than penalize those jurisdictions, which through sustained local efforts provide quality education . . . . "