Jessica Katz, a 7-month-old, seriously ill Soviet citizen, is the focus of an unusual effort by American citizens to keep her supplied with the proper food and to persuade the Soviet Union to allow her to leave the country for treatment.

Her parents are trying desperately to get her out of the Soviet Union and into the care of physicians who can treat her before permanent damage is done to her.

Jessica has been diagnosed by physicians in this country - working by telephone and through tourists - as having malabsorption syndrome, a rare and very serious disorder that prevents her from digesting and absorbing food properly.

Jessica is in jeopardy of physical impairment, including possible brain damage, and psychological disorders if she does not receive proper treatment -"the sooner, the better," in the words of Dr. Richard I. Feinbloom, a physician concerned with the case who is a member of the Harvard Medical School faculty.

Jessica is alive today because of the efforts of hundreds of people in the United States who constitute a network of financial, medical and moral support for her parents. Since March, when Jessica was described by a Boston physician as being "very sick," she has been sustained by a special formula carried to her by American tourists willing to make room in their suit-cases for bulky, one-pound cans of the only food that has enabled Jessica to gain weight.

Officials requests have been made by the State Department to allow Jessica and her parents - or at least Jessica - to leave the Soviet Union for treatment. No fewer than three hospitals - Children's of Washington, Children's of Cincinnati and Children's of Boston - have offered to treat her. Soviet officials, however, have refused to allow Jessica or her parents to leave.

Jessica's parents, Boris and Natalya, who are Jewish, applied in 1975 for exit visas to leave the Soviet Union for Israel. The visa for Mrs. Katz was refused on the grounds that she was privy to state sercets learned when she had worked as a computer programmer at the Soviet Institute of Experimental Meteorology and the Institute of Geophysics.

Boris' mother, Khaika Landman, and two brothers, Victor and Mischa, were able to leave and now live in Boston. As often happens with Russian Jews who apply for visas to emigrate to Israel, Natalya Katz lost her job. Boris continued to work, also as a computer programmer, at a job 75 miles from their apartment in Moscow, a distance that took him 2 1/2 hours to cover, so that he was home only on weekends. The Katzes continued their effort to leave.

When Jessica was born in October 1977, she seemed to be a healthy, normal child. In November, however, Mrs. Landman received a call from her son in Moscow. Her granddaughter was sick, suffering from chronic diarrhea, a rash and a large sore.

Landman called Judy Patkin, co-chairwoman of Action for Soviet Jews, a Boston group that is part of a network of groups across the country called the Union of Councils for Soviet Jews.

Ultimately, Patkin found Feinbloom, the Harvard physician. Working by telephone and through tourists who visited Moscow, Feinbloom began trying to get information about Jessica. The child had weighed 8 pounds at birth - a good weight - but had not benn gaining. The Katzes did not have a regular family physician and were having trouble getting medical treatment, according to Patkin. When the parents tried to get Jessica admitted to one of Moscow's children's hospitals. Patkin said, they were told there was no room.

"We were tearing our hair out over them - asking ourselves, "What can we do?" Patkin said in a telephone interview. On a Friday night late in December, Boris Katz called his mother again. Jessica had sunk into depression. She had cried before, but now she made no sound. She did not move.She was turning blue. Boris told his mother he thought his child was dying.

His mother telephoned Patkin, who called Irene Manekofsky, chairwoman of the Washington Committee for Soviet Jewry. An immediate phone campaign was organized, calling members of congress senators, Massachusetts Gov. Michael Dukakis, State Department officials - anyone who might be able to help.

In all those calls, Patkin said, "We always got a nebulous kind of answer. We don't know what they did." The next Sunday - "we'll never know how or why," Patkin said - Jessica was admitted to Moscow Children's Hospital Number One, which had rejected her previously. She was kept there until mid-March. Feinbloom continued to get information about her from her father, by telephone, and from tourists who visited the child in the hospital and brought back answers to questions.

But this process has not been satisfactory, according to Feinbloom. Katz has given him information from Jessica's health records that "indicates a lack of understanding of the problem" by the Soviet doctors who treated her, Feinbloom said.

"This is one area of medicine where I wouldn't be surprised if they weren't as advanced as we are here," he said.

By the time Jessica was released from the hospital, he was still "very sick," Feinbloom said.

"It looked as though the baby would not live if something drastic weren't tried," Patkin said. Based on the information available, Feinbloom judged that a predigested formula might help Jessica. Patkin got a prescription from Feinbloom and brought a 12-can case of formula from Boston Children's Hospital, paying $64 for the case.

The first six cans were sent in with a couple visiting the Soviet Union. One can sustains Jessica for about 2 1/2 days. Since that first shipment, there have been many more, as people from all over the country carried in the cans one or two at a time.

"The people who take a lot in were willing not to take many clothes in, to make that sacrifice," Patkin said.

Mead, Johnson, the manufacturer of the formula, donates what Jessica needs, shipping it to tourists who have offered to carry the cans to her. Patkin calculates that Jessica has enough to last her until July.

Patkin got the latest report on Jessica Wednesday by talking to Boris Katz on the phone. Jessica's weight had been up to almost 14 pounds, but suddenly she lost her appetite and had dropped 11 ounces. "You hold your breath," Patkin said. "You know she's very tiny. She can't afford to lose any weight."

American officials have discussed Jessica's case and that of her parents with Soviet officials a number of times. During Secretary of State Cyrus Vance's visit to Moscow in April, a State Department official said, the Soviets were given a list of several hundred Jewish "refusedniks," people who have unsuccessfully sought to emigrate to Israel. The Katzes were on the list, the official said. In addition, Jessica's medical problems were raised with a "senior Soviet health official" by a "senior embassy official." According to the State Department officer, the Soviet official said he would "look into it."