The District of Columbia is trying to collect about $18 million from the federal government in back claims for child foster care, but the city may get only a fraction of the money because it didn't file for payments properly and promptly.

In addition, the amount of future federal payments to the District for child foster care may depend on how successful the city's efforts are in obtaining the back payments.

The Reagan administration wants to put a cap on federal payments to local governments for such care, and plans to base the amount a local government could receive on how much it was paid in the past.

"A certain amount of the budget is riding on these claims," said City Council member Polly Shackleton (D-Ward 3), chairman of the Committee on Human Services. "If Congress bases future reimbursements on past levels , we could be in very bad shape."

The federal government pays 50 percent of the cost of foster care for children from families eligible for Aid to Families With Dependent Children. Almost all of the 2,000 children in foster care in the city are from families that meet AFDC eligibility requirements, city officials say.

The federal government requires that a local government notify it immediately when a child is placed in foster care for which the locality expects reimbursement. The local government must then document its claims and file for reimbursement.

Audrey Rowe, the city's Social Services commissioner, has conceded that the District hasn't always aggressively sought all the federal child care grants for which it was eligible.

For example, Rowe said, when the city filed for federal reimbursements for foster care in 1977, it applied for and received only about $300,000 when the city should have been eligible to receive about $1 million.

Although the city hasn't applied for reimbursement for child foster care for the years 1980 through 1982, it has, in some cases, notified the federal government when an eligible child was placed in foster care.

But more than half of the District's claims are for children about whom the federal government was not notified promptly, according to city and federal officials, and the federal government refuses to reimburse any locality in such cases.

The state of Pennsylvania is appealing that ruling to the grants appeals board of the U.S. Department of Health and Human Services. If the federal government's ruling against such back claims is upheld, the District automatically would be unable to collect more than half of its back claims, according to federal and local officials.

In the meantime, the city faces an April 1 deadline for providing proof for all claims for reimbursement for the years 1980 through 1982.

Sources familiar with the foster care program say the city may not be able to meet the federal deadline, noting that the city in the past has "lost" children in its paperwork.

Rowe maintains that a special computer system--developed by American Management Systems after a critical report of the D.C. auditor in 1980--can be used to document all the old cases.

Gary Koch of the U.S. Department of Health and Human Services' regional office, which reviews the District's claims, noted that the city has had problems documenting claims in the past.

"I think they the past claims were basically good guesses based on the number of children in care," Koch said. He said the city had trouble providing Social Security numbers, differentiating among children and getting a list of children.