Paternity Questions/Laws?

Married couple received a call from a female claiming that he may have fathered her child 13 yrs. ago during a one night stand. This was shocking to both! There are many unanswered questions, yet to come..however, female advised alleged father that he would be asked to take paternity test - this was after finding out that the person who thought was the father failed the test. What is the best advise on what would be the couples' best move. (if the DNA verifys that he is the biological father, after all these yrs. He will step up to the plate- but wants no court/custody/drama...doesnt know the mother's intention - after all, she may be a Ghetto Rat. Any advise?