A New Jersey dad has been ordered to pay child support for just one twin after a DNA test revealed that the other baby was fathered by another man.

Passaic County Judge Sohail Mohammad made the ruling in the paternity case on Monday, in what is one of only a handful of similar cases across the country.

It is possible - but rare - for a woman to give birth to twins with two fathers.

It happens when the woman has sexual intercourse with two men in the same week - during the same menstrual cycle - and releases two eggs. An egg is then fertilized by each man.

Rare: A judge in Passaic County, pictured, has ruled that a man must only pay child support for one twin after a paternity test showed he did not father the other; the mom admitted she had sex with two men in one week

The case came to light when a Passaic County woman sought child-support payments from a man she thought was the father of her daughters, who were born in January 2013.

Neither party has been named.

The mother, who was in a relationship with the man at the time of conceiving, admitted to having a sexual relationship with another man in the same week, the New Jersey Law Journal reported.

Paternity tests showed the man was almost certainly the father of one but wasn't the father of the other and he must now pay $28 per week, for just his daughter.

Mohammad says he found just two other court cases nationally on such matters.

An academic study in 1997 found that twins have different fathers in one out of every 13,000 reported paternity cases involving twins.