The Select Commission on Immigration and Refugee Policy yesterday recommended boosting the United States' permanent immigration Quota from the present 270,000 a year to 350,000.

The proposal, sponsored by Reps. Hamilton Fish Jr. (R-N.Y.) and Elizabeth Holtzman (D-N.Y.), also called for an additional 100,000-a-year allocation for five years to help clear up a backlog of admission applications from such countries as Taiwan, India, Korea, Canada, Mexico, the Dominican Republic, Britain and Nothern Ireland.

About three-quarters of the recommended 350,000 permanent total would be reserved for certain relatives of U.S. citizens and permanent resident aliens -- a family reunification preference.

The remaining one-quarter eventually would be allocated to a brand new category of general worker applicants who are ineligible for the family preference but seek to enter the country to better their lot or have special jobs skills needed here.

The recommendation for higher quotas was the key decision as the 16-member commission, created by Congress to study immigration and headed by the Rev. Theodore M. Hesburgh, completed its second day of voting here.

The acutal number of legal immigrants would be far higher than the commission's recommended 350,000 permanent quota and 100,000 extra slots for five years. In addition to immigrants who enter under the quotas (among whom are various relatives of permanent resident aliens), about 140,000 husbands and wives and minor children of U.S. citizens, as well as many refugees, come in quota-free each year. The refugee figure varies but was an estimated 366,000 in 1980, an unusually high figure. These non-quota entries would be permitted to continue.

Members of the commission said that by increasing legal immigration somewhat through the quota changes, the United States could reduce the pressure of illegal immigration and also, as Hesburgh put it, foster "diversity . . . the name of this country."

Spokesmen for Hispanic groups, such as the League of United Latin American Citizens, opposed creation of a separate set-aside for general worker applicants, unrelated to family reunificaton. There is already such a set-aside in the existing 270,000 quota but it is much smaller. The Hispanic spokesmen said the effect of the separate general worker category would be to bring in a larger percentage of middle-class workers and applicants from Europe and Asia, and cut the number of successful Hispanic applicants.

One result, said Joaquin Otero, vice president of the Brotherhood of Railway and Airline Clerks, is that the increase in the overall quota wouldn't really relieve the pressure of illegal immigration from Latin America.

In addition to its quota recommendations, the commission recommended:

Making it a crime, subject to civil and criminal penalties, for an employer to hire illegal immigrants. Such hiring is not now a crime, and the willingness of many firms to hire illegals is considered a major stimulus to illegal immigration.

Legalizing the status of 1 million or more illegal immigrants who were already in the United States before the start of 1980.

Continuing, with some changes, authority under which about 40,000 foreign workers enter the United States each year for temporary employment.