Yes, a DNA test that confirms he is not the father will stop him from having to pay it and anything he's paid in to it will be refunded. If he's not the father, unless he wants to and says he wants responsibility for the child, he's not responsible.
The thing with a DNA test is that it's not free and both he and the mother have to pay for it and submit to the testing, which could be as simple as a swab test or they could require blood to be drawn. A swab test is good enough.
This is how it works where I am in PA and I've had a DNA test done that proved I wasn't the father so while I truly do feel for the child involved I was and still am relieved I don't have to pay in to child support for a child that is not mine and don't have a relationship with (not by choice, I would father the child if the mother allowed it but she doesn't and didn't even when she accused me of being the seed).
The test cost $1500 and that cost was split between the mother and I. I had to go through the court system to have her ordered to take the DNA test because, of course she knew I may not be the dad, she didn't agree to have it done and going through court for it was another frustrating experience that thankfully ended in my favor. I was and he will still be responsible to pay the support payments until the test is done, results are determined, and a judge signs the waiver of responsibility release and that document is recieved and acknowledged.
It's not going to be quick. Prepare for a long frustrating path, especially if mom doesn't agree to the test voluntarily.
As I said I went through it in PA so the process may be slightly different but I've also lived in several states (and countries temporarily) and the laws between them all were generally the same so at least, and I hope, this gives you a general idea and some insight.