B6 or B16 would be the short end of the arbor that the chuck fits on to.
Does the arbor come out of the drill press spindle with the chuck? If so, you need to look for a chuck that comes with an arbor the right Morse Taper to fit your drill press spindle. Most would be a No 2 Morse Taper, aka MT2 or 2MT. Specs are online so you can look up from the dimensions on your arbor and see if it's MT1, MT2, MT3 etc
Or if you have the cheap drill press where the chuck mounts directly on the B6/16 taper that is integral with the spindle, you will need to buy a chuck with a tapered hole in it that matches. Specs for B6 and B16 tapers are online so you can measure yours and compare.