Jackson Champion, D.C. Republican mayoral candidate in the Sept. 12 primary here, proudly describes himself as "a third generation Republican," but he is having considerable trouble finding a home in his own party organization.

He ran for mayor as a Republican four years ago against Walter Washington, taking on the mayor without his party's blessing or endorsement. This year the D.C. GOP is taking on all Democratic mayoral candidates, but Champion, 55, is not the person party leaders have picked to lead the charge.

In a town where Democratic voters overwhelmingly outnumber Republicans, the dubious honor has gone to Arthur Fletcher, a newcomer to Washington politics whom Champion has labeled a carpetbagger.

"I'm asking Republican voters to look at my participation with the city and compare it with my opponent's," said Champion, who complained that his local party is being controlled by a small faction that discourages more involvement by rank-and-file party members.

Champion's long-shot chances at his party's mayoralty nomination have not been enhanced by the internal GOP dispute or by the fact that Champion has pledged to spend no more than $250 in the primary race.

But he is calling his a "people-to-people" campaign that he hopes will persuade enough Republicans and Democrats to throw the incumbents out.

"A republican administration is needed in D.C. to bring chaos out of the city government," said Champion, a former operator of a beauty supply business who now runs a publishing concern out of his Southwest home.

A native of South Carolina, Champion grew up in New Rochelle, N.Y., and was once publisher of a small community newspaper. He gave up a successful sales agency job and moved to Washington in 1971 after starting a national weekly newspaper designed to encourage developemnt of minority business.

Champion is a past member, by presidential appointment, of the board that oversaw the operations of the former Washington Technical Institute before it became part of the new University of the District of Columbia. He also authored a textbook/autobiography about his and other blacks' involvement in the Republican Party.

Ever critical of what he says has been the mismanagement of District of Columbia government, Champion said city officials should be doing a better job of providing employment and housing for poorer residents. He also has specific but controversial suggestions about how the District could increase its revenue sources.

"We should legalize gambling, so we could hold lotteries and have casino operations here," said Champion, adding that tourists in the town would have especially enjoy and patronize such activities. He would like to see voters decide the issue in a referendum.

Another Champion them, stated but not elaborated upon in his various campaign appearances, is a desire for the Republican Party here and nationwide to "regain an equal share of patronage, favoritism and contracts" in the political system.

Champion has said often he would rather run against incumbent Walter Washington in a general election because challenging either Council Chairman Sterling Tucker or Councilman at-large Marion Barry would make it a more difficult race for a Republican candidate.