President Carter's trustee purchased a parcel of land last month from his financially hard-pressed brother, Billy, for more than a quarter of a million dollars.

The transaction was negotiated for the 175-acre site upon which Billy Carter had planned to build a $750,000 "Mediterranean-style" mansion. The tract adjoins the president's two acres and modest home, according to a local architect.

The planned 16,000-square-foot house, with a swimming pool, solar-heated greenhouse and special quarters for presidential guests, was never built. The architect, William Cox, filed suit in nearby Marion County last August seeking $29,000 in unpaid designing fees.

According to Sumter County land records, Billy Carter paid about $610 an acre for the land in May 1975, and received more than 2 1/2 times that on March 1 from the president's trustee, Atlanta attorney Charles Kirbo.

A county assessor said the price paid to Billy Carter was reasonable, given the area's rapidly rising land values. Neither Kirbo nor the White House would comment on the land transaction.

Billy Carter's broker for the land transaction, Donald J. Carter, who says he is no relation but a friend of the Carters and Kirbo, said the property had not been publicly listed. He said no "For Sale" sign had been posted.

The transaction took place while Billy Carter was being treated at Americus-Sumter County Hospital for what was described as chronic bron-chitis. He has since been admitted to Long Beach Naval Hospital's alcohol unit, where he could not be reached for comment yesterday.

Courts records in Marion and Sumter counties show Billy Carter faces other potential legal problems.

In Marion, the Bank of Webster in Preston, Ga., sued him in January, claiming he refused to repay a $2,694.40 promissory note outstanding since March 1977.

Tax records in both counties show the Billy Carter family is delinquent in property taxes. In Marion, the Carters owe $940.14 since Dec. 20, and authorities say the matter will soon be turned over to the sheriff for collection. In Sumter, Billy Carter owes $324.68 since Dec. 20.

Billy Carter bought the 175 acres on May 19, 1975, according to Sumter County Records. He paid about $107,000, tax assessor Ron Greer says.

The 1975 land acquisition took place at a time of major changes for the Carters. Jimmy Carter was pursuing the presidency. And the Carter ware-house, then under Billy's management, was undergoing a major expansion.

In June 1975, not long after he became president of the National Bank of Georgia, Bert Lance arranged a $1 million loan to the Carters for a peanut sheller and a new warehouse.

The bank also extended a line of credit to the warehouse to finance peanut purchases from farmers. The largest loan extended at the time by NBG, the credit line portion, reached $2.2 million in 1975 and $3.7 million in 1976.

Lance's banking affairs are under federal grand jury investigation in Atlanta. That investigation has touched on the Carter warehouse loans and the Justice Department is now considering how to pursue the matter.

Kirbo, the President's trustee, said he would not comment on the purchase of Billy Carter's 175 acres until the Justice Department concludes its probe of the warehouse loan.

Cox, the architect for the mansion that was never built, said his first drawings rendered in early 1976 called for a 9,000-square-foot house. But under the directions of Sybil Carter, Billy's wife, the plans quickly expanded to the 16,000-square-feet dimensions, he said.

Cox said the Carters made an initial $5,000 payment before Christmas 1976. That was the last payment he received, Cox said.

Cox, who said the house was "as good as anything you'd find in Holly-wood or anywhere else," included at least one unique feature in the design.

He says that peanut gravel from the surrounding fields was to be used for the patios and terraces and included in the house's stucco and cement finish. "Nobody in the world had ever done this," he said.

Carter's attorney, John Parks, noted there was no contract signed for the architectural drawings. He said that the payment made at Christmas 1976 covered all the work that Cox had been authorized to do.

Cox said he learned secondhand that Billy Carter had purchased a home in nearby Marion County. It is a sprawling brick house at the top of a hill, set back one-quarter of a mile from the main road.

Meanwhile, Billy Carter has been unable to find a purchaser for his former house, which is on the market for $68,000, according to the broker.