is there any way you can get a paternity test for free

I know that getting a paternity test or what-not can take weeks but I was always under the impression this was more the waiting list than the actual doing of the DNA test. If so, how long would a piece of DNA evidence take to be tested? Would it depend on the quality of the DNA sample?

Someone goes around telling everyone that ya fathered their kid, but refuses to do a DNA test. Can ya force a paternity test to settle the issue?