Yes it is possible - though it varies by state (assuming OP is in the USA) and usually has a statue of limitations. In my state they could sue for up to 5 years following the child's 18th birthday. There are stories of people finding out years later that they have a kid when the kid's mom files for benefits and names them or finally decides to tell them and cash out. They then get slapped with back child support and garnished wages. It will depend on the circumstances and the local laws. But there have been women who wait till the kid is 18 so you can't challenge custody and then sue for child support. Moral of the story: wrap it before you tap it, even if she says she's on the pill, and make sure to take responsibility for birth control as a man, because otherwise your past could come back and bite you in the ass 20+ years later.