DNAmned if you do and DNAmned if you don't
In other words, it may not exactly be a "stroll on Easy Street" for you no matter what da result of da paternity-test shows --- a prime example would be dat even if said test does indeed prove dat you're not da love-baby's daddy, da test's in-da-thousands-of-dollars cost may be somewhat comparable to what you'd have hadda spend for child-support, anyway.
Good luck on getting a refund for da momentous cost of a paternity-test if said test proves dat indeed you are not da child's biological father (see "pap smear", definition #14); you might be better off to simply start making support-payments; it can definitely be a "DNAmned if you do and DNAmned if you don't" situation!