The Senate, moving forward on a major immigration reform bill, rejected a proposal by Sen. Edward M. Kennedy (D-Mass.) yesterday to expand the number of illegal aliens eligible for an amnesty program and to grant the amnesty at the same time employer penalties go into effect.

The vote of 65 to 26 came as the Senate completed its third day of debate on the immigration package, which is expected to come up for a final vote early next week.

In another major change, the Senate approved by a voice vote an amendment by Sen. Paula Hawkins (R-Fla.) to require states to verify an alien's legal status before approving welfare, food stamps, Medicaid and unemployment benefits. Hawkins estimated that the measure, which is supported by the Immigration and Naturalization Service, would save taxpayers about $10 billion per year.

Senators also added to the bill, by a 51-to-39 vote, an amendment by Sen. James A. McClure (R-Idaho) to require a warrant before federal immigration officers can search an open field. The measure had been promoted by growers and civil liberties advocates, but strongly opposed by the Reagan administration and the INS.

"Farmers should be awarded the same rights and standards of protection" as other businessmen, McClure said, adding that under his amendment, "Employes would be protected from the humiliation of impulsive interrogation by the INS."

Simpson, who opposed the amendment, argued unsuccessfully that the Supreme Court has ruled a warrant is not needed to search open fields and that the change would "severely hamper" INS agents trying to enforce the law.

Another Kennedy amendment, which won approval on a voice vote, could lead to termination of legal penalties against employers of illegal aliens if those penalties were found to cause widespread discrimination against workers of Hispanic descent.

Under the proposal, the General Accounting Office would investigate whether sanctions resulted in a widespread pattern of discrimination. After three years, Congress could either eliminate the sanctions or adopt new antidiscrimination protections.

Kennedy's defeated amnesty amendment had been supported by Hispanic groups who want legalization to occur simultaneously with the employer sanctions. Under the Simpson bill, the sanctions would take effect a year after enactment, with legalization postponed for up to three years while a commission studied whether illegal immigration was being reduced under the new law.

They have charged that employers would not hire Hispanics or others with foreign-sounding names if they could face civil fines and criminal penalties for knowingly hiring illegal aliens.

Simpson's version also restricts amnesty status to illegal aliens who have been in the United States continuously starting before Jan. 1, 1980. Kennedy tried to include more people in the amnesty, by moving the cutoff date to those in the country since Jan. 1, 1981.

Several controversial items remain to be decided when the Senate resumes debate Monday, including the question of whether the federal government will pick up the cost of social services for the newly legal aliens. Several states, including Florida, California and Texas, are expected to be disproportionately affected by such costs.

In addition, Sen. Pete Wilson (D-Calif.) is expected to introduce a new version of an amendment defeated Thursday by the Senate on a 50-to-48 vote that would create a new program to allow foreign workers into the country on a temporary basis to harvest perishable crops.