So they relinquished custody of the newborns, who are identified only as Baby A and Baby B in a federal lawsuit filed by the couple alleging that their embryos were swapped or misplaced, forcing the woman to carry other people’s babies to term in a successful in vitro fertilization that nonetheless went terribly awry.

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The civil claim, filed last week in the Eastern District of New York, accuses the Los Angeles-based clinic where the pair sought treatment, as well as two men whom the lawsuit identifies as the clinic’s co-owners and directors, of medical malpractice, negligence, battery and intentional infliction of emotional distress, among other counts. It seeks compensatory as well as punitive damages.

The clinic, CHA Fertility Center, did not return a request for comment Sunday. The defendants had not made any filings in the case as of Sunday. An attorney also didn’t immediately return a request for comment.

The July 1 complaint identifies the plaintiffs, residents of Queens, by their initials, in an attempt to protect their privacy. The woman is A.P., and the man is Y.Z.

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Ever since their marriage in 2012, the couple has yearned for children. Specifically, their wish has been “to conceive, deliver and raise children of their own,” as their lawsuit claims. Their attempts to conceive a child were unsuccessful, so they turned to different strategies, including artificial insemination. But natural as well as alternative measures left them disappointed.

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The pair learned of CHA Fertility in late 2017, as the court filing recounts. They reviewed the clinic’s website, as well as its promotional materials, which tout its services as among the “premier fertility treatment networks in the world," according to the lawsuit.

Its doctors “evaluate patients on a case-by-case basis to ensure each receives the most appropriate and advanced treatment necessary,” claims the center’s website. CHA promises “personalized care,” at the heart of what it says are its “high success rates.”

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The center is led by doctors who have won accolades for their research and clinical work.

According to the most recent data published by the Centers for Disease Control and Prevention, fertility clinics in the United States conducted more than 263,000 cycles with assisted reproductive technology in 2016. Of those, about 81,000 resulted in pregnancies, which led to nearly 66,000 deliveries.

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The report on the 2016 data, produced by the CDC last year, noted that success rates depend on the type of procedure — the most common of which is in vitro fertilization — as well as the age of the woman and her history of prior births and miscarriages, among other factors. A study published in 2015 in the Journal of the American Medical Association, which looked at a sample of thousands of women in Britain undergoing in vitro fertilization between 2003 and 2010, found that more than 65 percent had a child by the sixth try.

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A.P. and Y.Z. traveled to CHA Fertility in January 2018, according to the lawsuit.

Y.Z. produced sperm, while A.P. took on a regimented schedule for the growth of her eggs. She returned to the center the following month for egg retrieval. The couple claims that they paid more than $100,000 for facility fees, medication, laboratory expenses, travel and other costs.

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In February 2018, a set of embryos was formed and tested, showing that five had complete sets of chromosomes. Clinic staff froze the embryos for preservation, as court records document. A.P. proceeded to follow a protocol for undergoing in vitro fertilization, which included submitting to testing and consuming medications and prenatal vitamins.

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Last summer, she returned to the fertility clinic for embryo transfer, using one of the female embryos formed in February. But she didn’t become pregnant.

The couple tried again the following month, working with medical providers at the clinic who said they would thaw two more female embryos for transfer, according to the legal claim.

A.P. learned from her OB/GYN last September that she was pregnant with twins. She and her husband were “ecstatic,” the lawsuit states.

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Then, questions arose. When sonograms were taken at three and five months, the couple learned that two boys were on the way. This news was at odds with what doctors at the clinic had told them — that there was only one male embryo in the set, and that it had not been among those used in the transfer.

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According to the lawsuit, the couple raised the findings with clinic doctors, who told them the sonogram result was “not accurate and that it was not a definitive test.” One of the doctors said his own wife had been informed, based on a sonogram, that she would be having a boy only to give birth ultimately to a girl, the lawsuit asserts.

In March, A.P. gave birth to male twins in a hospital in New York. Neither was Asian.

DNA testing confirmed that neither member of the couple was related to the newborns. The results further showed that the newborns were not related to each other.

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“Plaintiffs were required to relinquish custody of Baby A and Baby B, thus suffering the loss of two children,” according to their claim. “Plaintiffs have suffered significant and permanent emotional injuries for which they will not recover.” It further asserts that A.P., who carried the babies, suffered “physical and emotional injuries.”

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The lawsuit doesn’t speculate about how the transfer went wrong but accuses experts at the fertility clinic of trying to conceal the alleged error from the aspiring parents. It claims that the clinic contacted two other couples who enlisted CHA’s services, determining that they were the rightful parents of the two babies.

As for what happened to their original embryos, the lawsuit claims that the clinic’s doctors have left the couple in the dark.

Faulty embryo transfers have led to lawsuits against fertility clinics in the past, including one this spring targeting a now-defunct facility in Trumbull, Conn. In a markedly different scenario, a New York mother last fall actively sought to trade a female embryo she had preserved for a male version, saying she wanted to give her son a brother.

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A trade was not the expectation — and certainly not the intention — of the couple from Queens.

In addition to medical malpractice and negligence, their lawsuit against the Los Angeles clinic alleges intentional infliction of emotional distress, reckless and wanton misconduct, breach of contract, battery and other wrongdoing.

The claim describes the conduct of the clinic and its leaders as “extreme and outrageous.”