The East of the River Health Association Inc., which operates a community health clinic here, said yesterday it plans to offer free and low-cost health-care services to 13,000 District of Columbia residents who have lost their jobs since Dec. 1, 1981.

Under a new program funded by a $303,523 grant from the federal Department of Health and Human Services, the health association is offering a wide range of services to unemployed residents and their families at a cost not to exceed $5.40 per visit, said executive director James T. Speight Jr. An average doctor's visit in D.C. costs about $35, he said.

"Since we received the grant money in July, we have hired additional doctors, nurses and auxiliary staff. Now, we have to go out and find the people who lost their jobs and make sure that they're getting adequate health care," Speight said.

"We have seen many cases where people have put off going to the doctor because they did not have the money to pay for health care," Speight said.

"By the time they came into the clinic, their problems were critical. This program should deter that type of self-neglect," he added.

The money for the program came through the Emergency Expenditure to Meet National Needs Act of 1983, also known as the "jobs bill."

The health association operates a large clinic at 5929 East Capitol St. as well as two satellite offices at 21st Street and Benning Road NE and at Hadley Memorial Hospital's Family Health Services Center, 4601 Martin Luther King Jr. Ave. SW.

The nonprofit association suffered a $250,000 cut in its annual budget last year, which left it with about $830,000. The association sees about 9,000 patients each year and handles about 25,000 doctor's visits, Speight said. He said that under the program, an additional 1,300 patients are expected to visit the clinic and its satellite offices.

Speight said that although any unemployed D.C. resident who has lost a job since Dec. 1, 1981, is eligible for the program, the association has targeted residents in Wards 5, 6, 7 and 8, which comprise most of Southeast and Far Northeast where there is a high density of poor and unemployed people. "On Monday, we will be sending out 26,000 letters to people who live in those areas," Speight said.