Yorkville: paradoxical New York City neighborhood where ultrarich and ultrapoor live side by side, yet rarely meet

There is an oasis in a cold city, Where a few of beauty show true pity. Theirs is the goodness to make us cope,

In them is the glorious beauty of hope.

- Jack Fox

Jack Fox, who lives in a nearby mission, is referring to the public school here on East 91st Street that provides hundreds of neighborhood residents with clothing, job counseling, and hot meals. But it is ironic that this ''oasis,'' as Mr. Fox (who is not a professional poet) calls it, is located in New York City's wealthiest community, Yorkville.

The Yorkville area, also known as the Upper East Side, runs between 59th and 96th Streets and is bordered by the East River and Central Park. Among its 225, 000 residents are some of the richest and most influencial people in the world; its high-rise apartment buildings and well-scrubbed town houses are home to bankers like David Rockefeller; lawyers; artists and patrons of the arts; figures from the broadcasting world like Dan Rather and Charles Collingwood.

But quite a different picture emerges on some of the side streets, as the high-rise landscape drops dramatically into rows of jagged, early 20th-century tenements.

The age and delapidated condition of these tenements is an indication that the problem of the Yorkville poor did not begin with the Reagan administration's push to cut federal social-service costs nationally. Some 7,000 Yorkville residents lived below the ''Federal Standard Poverty Level'' before Mr. Reagan took office, according to the Yorkville Emergency Alliance. The YEA is a private , nonprofit group fostering cooperation between government-sponsored community human-service agencies and volunteer and business organizations.

But as federal dollars for New York City as a whole began to dry up and city officials began to view the Yorkville's needs as far less acute than those of Harlem and other areas, the social-service problems facing Yorkville reached a crisis stage.

''The crisis was brought on by a whole new social and fiscal policy emanating out of Washington,'' says Rabbi Ronald Sobel of Temple Emanuel, a synagogue on Fifth Avenue, the wealthy western fringe of Yorkville.

''We really didn't know what these new fiscal and social policies were going to mean a year ago,'' Rabbi Sobel continued, ''but we knew it was going to have some effect.''

Some of the effects are evident at the school on 91st Street, where Mr. Fox recently went to get a hot meal. He wrote his poem on a scrap of paper on the school lunch table, out of gratitude. For most of the hundreds of others who stream in here two days a week, their actions and appearance speak just as loud as Mr. Fox's gracious thoughts. Some are relatively well-dressed young men who have recently been laid off. They are often the first in line when the food is served and often the first to leave. They talk to few. Some, looking furtively from one side to another, seem worried they will be seen by their neighbors.

Sara Weaver has to look after three grandchildren. She has ''no kind of income,'' she says, because she and the children are squatters in a tenement a little farther uptown. Since she pays no rent or electricity bill, she says, she has been declared ineligible for welfare.

A soft smile appears on the face of another woman when a social worker tells her she will be able to get proper winter clothes for her two young children.

Community workers say many well-to-do Yorkville residents are ignorant of the plight of their neighbors.

''It's often easier to think about what you can do for somebody in the Middle East or in Africa than somebody right next door,'' says Alan Houghton, pastor of the Church of the Heavenly Rest on 92nd Street, which operates its own ''soup kitchen'' several days a week as well as a day-care center.

In a special series of meetings and televised appearances, members of the YEA are hoping to rekindle community interest in the welfare of the entire community. But activists like Carol Tweedy, the director of the Stanley M. Isaacs Neighborhood Center, say this ''message'' must be driven home to Washington, too.