Former Pennsylvania congressman Peter Kostmayer is continuing to handle constituent inquiries even though his term expired nearly three months ago, and his Republican successor is crying foul.

In a brief letter to the two-term Democrat, whom he defeated in November, Rep. James K. Coyne demanded that Kostmayer hand over any files related to active constitutent services.

Helping constituents unsnag problems with the bureaucracy, such as obtaining Social Security payments or getting a child into a service academy, is casework that is particularly critical for winning elections.

Kostmayer, who now is employed with the Congressional Management Foundation, has said he may seek either his old House seat, or take on Sen. John Heinz (R-Pa.) in 1982.

A former aide to Kostmayer, who maintains an apartment in Washington, contends that any unresolved cases at the time of the election were concluded "within a week or two."

But Hugh Coffman, Coyne's administrative aide, alleges that Kostmayer has been "misleading" former constituents by continuing to contact federal agencies on their behalf, using a letterhead bearing his name and the subtitle, "Member of Congress."

Ed Mitchell, Kostmayer's former administrative aide, pointed out that any citizen may intercede on another's behalf and that, at any rate, Kostmasyer is entitled to continue to use his mailing privileges as a former member of Congress for 90 days after leaving office. That period will end April 3.

"Action Lines and clergymen do this all the time," Mitchell argued. "You don't have to be a congressman to do this." He said Kostmayer receives "a few" calls each week from former constituents asking for his help.

But Coffman scoffed at those claims. "I don't think a former congressman has the position of a priest, and I don't think he's functioning as a reporter or consumer advocate."

Coffman said that when the office first opened in January, he asked Mitchell to turn over any active case files. He said Mitchell told him that none existed. Coffman said office aides expressed concern after receiving several complaints from constituents that their cases were being ignored.

Should Kostmayer refuse to hand over the files, Coyne plans to introduce legislation that would force him to do so, Coffman said.

"The files," he said," belong to the Eighth Congressional District."

"The mail," Mitchell rebuts, "belongs to Peter Kostmayer."