The key question about an at-home paternity test is the purpose for the test. If you are trying to establish a legal case that you are or are not the father of a child, an at-home paternity test will not be a good idea. Because the sample process is uncontrolled, the tests are not admissible in court. So you will need to go to a facility where the sample process is supervised.
If, however, you want a paternity test for your own peace of mind, an at-home kit is an acceptable and cost effective alternative. At-home paternity testing kits can be purchased at local stores or online.