PATERSON, NJ -- A paternity case involving a set of twins had a surprise ending worthy of a daytime TV talk show: the girls have different dads.A judge ruled Monday in a paternity case that the man from whom the twins' mother sought child support has to pay for only one of the children. A DNA test showed that he was almost certainly the father of one twin, but wasn't the father of the other.It's rare for a woman to give birth to twins with different fathers, but can happen naturally. The phenomenon, called heteropaternal superfecundation, can occur when a woman produces two eggs during her fertility cycle instead of one, and they can become fertilized and implant within a few days of the same cycle."The sperm live in the genital tract for two days," Dr. Brooke Rossi told ABC News . "It's possible a woman can have sex with a man on a Tuesday and have sex with a different man on Wednesday, and it is possible for [her] to get pregnant."An estimated one in 13,000 paternity cases involves twins with different fathers, according to a 1997 medical journal cited in the court ruling. Passaic County Superior Court Judge Sohail Mohammed wrote in his opinion that nationally, he found two other court cases on such matters.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. In court testimony, the mother said she had sex with two men in a span of about a week, but only one was listed in her petition for child support. The judge ruled that the man owes $28 per week for only one of the children.