Oxycodone is a member of the opioid family of narcotics. All members of this family resemble and behave like morphine and are used for the management of severe pain. Oxycodone is probably more commonly know by its trademarked name OxyContin. In the US it is listed as a schedule 2 controlled substance and is available only by prescription. Like all opioids, the biggest danger with oxycodone is the fact that it is extremely habit forming (meaning addictive).
Drug testing comes in many different forms. Some tests are quick tests of urine samples in a doctor's office that test for general classes of drugs. One of the classes tested for are opioids. These quick tests can be cheap and give false positives. If this is the case, then you would have gotten a false positive for opioids, but not oxycodone specifically. A test of this nature could never identify with that kind of specificity what drug it is detecting. A proper drug test involves shipping a sample to a lab with equipment like mass spectrometry and gas chromatography to test for very specific drugs in a person's sample. I believe that this is the only way to test positive for something like oxycodone. So find out what kind of testing was performed. If it is a cheap, quick, in the office test then request a proper drug test as a follow up. A false positive would be much, much less likely under those conditions.