When we discussed prenatal testing before, you asked how reliable it is, and I said it totally depends on who you use, and suggested you look up consumer reviews on the lab you intend to use, suggested you should test with both guys, and cautioned that women who test with only one guy will often write in and ask, "What if the test is wrong?" You didn't use those words but you are worrying about accuracy.
If you get an answer you don't think is right, all you can do is test again. But my suggestion is to use a lab that has better ratings, such as Ravgen or the DDC, and if they are too expensive, just wait until the baby is born and test at a lab approved by the courts in your area of jurisdiction for determining paternity legally.
We've discussed the question before, and it all hinges on whether your doctor was correct in counting forward two weeks from your last period, to tell you that January 3 was your likely conception date. Some women do ovulate a couple of weeks after their last period. Those are women who have super regular cycles about 28 days long from period to period. If a woman has more irregular cycles, or longer cycles than 28 days, or shorter ones, then it's anyone's guess when she might ovulate in a given month.
Good luck with the test results!