Re: false positive hepatitis b test from the vaccine?
According to the CDC, if you've had the vaccine but not the disease, you should have a negative result on HBsAg, but positive on anti-HBs. Positive result on HBsAg usually means you actually have it, that the test found virus floating in your bloodstream. Positive anti-HBs means you are immune, that you have antibodies to the virus.
You doctor hasn't provided enough information. Go back and ask what exactly the test showed.
If HBsAg is positive, but you are not sick, the doctor will most likely recommend repeating the test in a few months. It's possible the test was just plain wrong, or it could be the virus is in you but your body is successfully fighting it off.