It’s called superfecundation– while fertile, if a woman sleeps with two men during the same fertility cycle, she can conceive twins from two separate fathers. This is not very common, but it is not impossible. 1 out of every 13,000 cases involving twins involves superfecundation.
In New Jersey, a woman tried to collect child support from a man she believed to be the father of her twins. She was right, but only half right. DNA Test Results proved he was only the father of one of the twins, but not the father of the other.