Hamuli Rety has never seen his 4-year-old son. The boy, who lives in the Washington area, knows only that he is adopted. He has no idea that his father, a native of Zaire, is a prominent young lawyer in Paris.

The child's mother gave the child up for adoption in 1983, and the boy has lived with his adoptive parents since then. They are the only parents he has known.

Now Rety is pressing his claim for custody of his son before the D.C. Court of Appeals, and the outcome could plow new legal ground in the areas of competing custody claims, adoption and the termination of parental rights.

Rety's lawyer, Thomas C. Jones Jr., who has handled the case without charge for more than two years, said that whichever way it is decided it "should definitely make new law on fathers' rights."

In some respects, the case comes down to the competing interests of the father and child, who is known in court papers as Baby Boy C.

Rety and the adoptive parents take absolutist positions that cannot be reconciled: Rety says the state has no power to terminate the rights of a parent who is legally fit, and the adoptive parents say the court must decide the question in the best interests of a child who could suffer emotional trauma by being taken away from them.

The issue is important because it goes beyond the quirky, one-of-a-kind nature of the case.

Art Peterson, an assistant state attorney general in Alaska and a noted adoption law expert, said the case "is an extremely difficult one."

He said a series of U.S. Supreme Court cases on the subject leaves open the question of how Rety's case should be decided.

Rety, 34, was in Washington yesterday to listen to arguments before the appeals court. The public session was the first in an otherwise closed family division case. Jones told the court that Rety was not given legal notice of the adoption proceeding for 596 days after his son was born.

Under District law, an unmarried father must be given notice of an adoption proceeding started by the natural mother. The law presumes the father to be the proper person to have legal custody unless he is shown to be unfit.

Jones argued yesterday that Rety's case was a sham, a "fraud on the court," because the adoption agency, the Barker Foundation, sent him misleading letters that did not inform him that an adoption case had been filed or that he had any legal rights with regard to it.

David Klontz, a lawyer for the agency and the adoptive parents, acknowledged that Rety had not been properly notified, but he said it really doesn't matter now because the child has been with his adoptive parents for five years. If Rety has a case, Klontz said to an apparently surprised three-judge panel, it is a suit against the adoption agency for civil damages.

Klontz said that Rety's own expert had testified that removing the child from his adoptive parents would have a "devastating" effect.

Rety said in an interview after the hearing that it is important that his son knows his African heritage. "Unlike other children of his color in this country, he has the chance to know his roots," he said.

Rety said he met the child's mother in his hometown of Bukavu, in eastern Zaire. The woman, who is identified in the case only as LC, was a birth control counselor for the Peace Corps, Rety said.

Although he was already engaged to another woman, Rety said he became very much involved with LC, and he described their tearful parting in November 1982 when he returned to school in Kinshasa. It was at that meeting, the last time he saw her until a Superior Court hearing here three years later, that she became pregnant, Rety said.

They exchanged letters, he said, and she returned to the United States, telling him she would have an abortion, Rety said. Then, in October 1983, he learned that a son had been born in August. Rety said that LC also told him that she had given the child up for adoption and that he had no rights in the matter.

Judge Judith W. Rogers, in questioning Klontz, posed the question that the court will have to decide: "If the state doesn't like what I'm doing with my child, can it just step in?"