In a poignant case that has bitterly divided three generations of an Oklahoma family and judges of the state as well, the Supreme Court has been asked to decide whether a child will grow up with her mother and stepfather or with the grandmother who obtained custody of her with an alleged fraud.

The child, Lori, now almost 11, was born out of wedlock to Kitty L. Winter, then 17, in July 1968. Yielding to considerable pressure from her parents, Robert D. and Bette J. Winter, with whom Kitty and Lori lived for 2 1/2 years in Shawanee, the young mother allowed them to adopt the child.

The adoption gave Lori the advantages of a two-parent home, a birth certificate listing Robert and Bette as her legal mother and father and medical and health insurance.

But in exchange for her consent to the adoption, Kitty obtained a promise from her parents: to restore her parental rights if she were to marry a man acceptable to them.

Shortly before the adoption decree became final in February 1972, Kitty married an Air Force trainee, now Sgt. Robert Strouse. Because the grandparents approved of him, Kitty requested them to return Lori to her.

But for 2 1/2 years afterward, Bette offered repeated excuses for holding on to Lori, claiming that a favorable time would come someday.

Finally, in July 1974, Bette admitted to Kitty that not only would she never give up Lori but had never intended to do so. This, Kitty alleges, was the first revelation that her mother's promise had been a fraud. Bette denied having made a promise in bad faith, but state trial and appellate courts rejected her version.

In March 1976, Kitty sued for a court order to set aside the adoption and to regain custody of Lori. The trial judge ruled for her and allowed her to take the child to Wichita, Kan., where her husband is now assigned.

Kitty's father, a cross-country tractor-trailer driver who was by now divorced from Bette, supported his daughter. But Bette appealed to the Oklahoma Supreme Court.

By a 5-to-4 vote last October, that court reversed and ordered the restoration of Lori to Bette Winter.

In a petition for review by the U.S. Supreme Court, Kitty's lawyer, Maurice H. Merrill of Norman, Okla., said that the net result would be "to deprive Lori of the comfort of the care of a father; and as well to subject her to the pressure of the grandmother who is bitterly estranged from her mother and will endeavor to alienate Lori's affections from her.

"The adverse psychological effect upon Lori will be tremendous," Merrill said. "It could destroy her chances for a well-adjustred life."

The state court's reversal was based on a 1971 state law that bars a challenge to an adoption more than a year after entry of the final decree.

Kitty contended that her mother's fraud overcame rhe restriction. But in the opinion for the majority, Judge Pat Irwin wrote that under state law Kitty had a year in which to sue after discovering the fraud, but had delayed for more than a year and a half.

In the dissenting opinion, Judge John B. Doolin accused the majority of ignoring the intent of the state legislature when it enacted the adoption law. "It was not designed with the intent to protect adoptive parents who act out a clear course of fraudulent behavior in intimidation and coercion and outright lies as practiced by Bette," Doolin said. He added:

"Bette not only defrauded her daughter Kitty, she lied and misled the trial court as to the basis Kitty's consent to the adoption. Because of the fraud she perpetrated, there are no public policy considerations which favor allowing this adoption to stand . . .

"Fraud was practiced on the [trial] court to the detriment of Lori. The trial court found her best interests were served by her return to Kitty. Lori is certainly blameless. Her welfare must not be ignored."

Although Lori did not testify, an attorney for her mother said that the child repeatedly has expressed a preference to remain with hermother and stepfather in Wichita.