A dozen sponsors and contractors in New York City's federally sponsored summer lunch program for needy children were indicted yesterday on fraud charges after an undercover FBI investigation.

The inquiry began in the summer of 1979 when a Buffalo businessman, Paul Snyder, was told he would have to pay kickbacks to get summer lunch contracts in New York. Snyder said in a telephone interview that he went to the FBI instead and allowed agents to use the cover of his firm to infiltrate the network of private sponsors and contractors who allegedly billed the government for food that never was delivered.

The operation was code-named "Apple Core" and for months the undercover agents secretary taperecorded transactions and witnessed alleged payoffs, an FBI official said.

Although the indictments yesterday charged only about $200,000 in overcharges, Robert Magee, acting inspector general of the Agriculture Department, said his office has estimated that as much as 20 percent, or more than $20 million, of the $120 million-a-year program is stolen.

"It's one of our smallest feeding programs but it's the most troublesome," he said, because it is run by private groups instead of the public schools, which administer most feeding programs.

Among those indicted yesterday were the director of the program of the Church of God in Bronx, officials of a day care center, a trucking firm, and a former assistant district attorney in Brooklyn. The trucking company, for instance, was accused of falsifying invoices for 100,000 meals it never delivered.

The inspector general's office at Agriculture has complained for years to Congress about the operation of the summer feeding program. In one instance last summer former inspector general Thomas McBride supported Sen. Henry Bellmon (R-Okla.) in an unsuccessful attempt to amend legislation to kick large private sponsors out of the program because of the history of abuse. Sen. Jacob K. Javits (R-N.Y.) killed Bellmon's amendment.

Agriculture's Magee noted that a 1976 effort to tighten the program in New York resulted in cutting its cost in half -- apparent evidence of inflated billings -- without affecting the number of children served.Past abuses also have included sponsors providing spoiled food or substituting sweetened, orange-colored water for orange juice.

Several individuals already have pleaded guilty when confronted with the evidence gathered by the undercover agents in this case.