Wiliam B. Cummings, the Alexandris-based federal prosecutor appointed by President Ford four years ago, said yesterday he will not seek reappointment from President Carter.

His announcement touched off speculation about whom the Carter Administration will seek to appoint and what role Virginia's senior senator, Harry F. Byrd Jr., will play in the appointment process.

Cummings, 39, who said his resignation will become effective June 1, is U.S. attorney for the Eastern District of Virginia, an area with a population of about 4 million that includes the Washington suburbs, Richmond and Norfolk. He is one of only four Republican prosecutors chosen by the previous administration still serving.

Among those mentioned yesterday in Virginia political and legal circles as expressing interest -- publicly or privately -- in the $46,600-a-year-job were William S. Burroughs Jr., the Arlington commonwealth's attorney; John T. Schell, a Fairfax lawyer who ran unsuccessfully for the Democratic nomination as Vcirginia attorney general several years ago; Anthony Troy, a former Virginia attorney general, Robert Williams, an assistant U.S. attorney in Norfolk, and William P. Williams, a Norfolk lawyer who is a law partner of State Sen. Peter K. Babalas (D-Norfolk).

Burroughs declined comment yesterday. William Williams and Schell confirmed that they are interested in the job. The others could not be reached for comment.

Sen. Byrd, a Democrat-turned-independent who has been at loggerheads with the administration recently concerning the selection of federal judges in Virginia, said yesterday he would "probably" give an opinion on a successor to Cummings if Carter asks him to, according to an aide.

The aide, Jack Davis, said Byrd would not lobby the administration on behalf of anyone, and had not been asked to do so.

The cooperation of Byrd is crucial to the speedy selection of a new federal prosecutor because of the doctrine of "senatorial courtesy." Under that doctrine, the senior senator of a state can kill a nomination by voting against it, knowing that other senators will respect his wishes.

An aide to Attorney General Griffin T. Bell said yesterday "we will have to be assured that Sen Bvrd will not disprove" of a candidate before sending his name to the Senate.

Terry Admson, a special assistant to Bell, said that at this point, "Frankly, we haven't given very much thought to a successor" to Cummings.

Cummings was praised yesterday by current and former colleagues and lawyers as a fair and capable trial attorney and administrator.

Among those successfully prosecuted by Cummings and his staff of 30 attorneys were the giant Allied Chemical Co. for pollution caused by the pesticide Kepone and Vietnamese expatriate David Truong and former government official Ronald Humphrey, both accused of espionage.

Cumings plans to set up a private law practice in Alexandria.