Edward G. Winner, chief finance officer of the D.C. public schools, has been asked by Mayor Marion Barry to give up his school position to help straighten out the city's troubled financial management system.

Colin F. S. Walters resigned as the city's top money manager after Barry and city administrator Elijah B. Rogers expressed dissatisfaction with the way his agency was run.

Winner said yesterday he would be willing to leave his $52,557-a-year post as the school administration third-ranking officer, and take the job of assistant city administrator for financial management.

Winner would be joinng the Barry administration at a time when the city is facing a $28 million budget shortage for the balance of this fiscal year. Its financial woes are further compounded by this week's D.C. Court of Appeals ruling which requires the city to refund up to $58 million it has collected from such professionals as lawyers, accountants, engineers and architects who do business in the city.

But most of Winner's duties apparently will be to work out the kinks of the city's new financial management computer system.

Winner, a former English teacher and Washington native, has been in charge of all business operations for the school system -- including budget, finance, personnel, food services, transportation and buildings and grounds -- since 1975.

Calling Winner "the backbone of (superintendent) Vincent Reed's administration," school board president R. Calvin Lockridge accused the mayor of "robbing the school system of one of its most knowledgeable employes." m

Barry has tapped numerous school officials to fill key positions in his administration.