You don't need a quill adapter on a threadless headset. There are no threads holding the fork in place. The fork goes through the headset you will need an adapter to get the fork steerer that is above the headset to 1 1/8th inch diameter to allow the stem to clamp to the steerer. Install the fork through the headset install the adapter over the protruding steerer install spacers and stem to get desired height. You will need a stem plug/ star fangled nut at the top inside of the steerer. Install more spacers above the stem untill the top of the steerer is a 1/4 inch or more below the top of the spacers. screw the cap and cap bolt into the nut tighten until the play is gone from the fork align and tighten the stem bolts. If there is a lot of steerer above the top of the stem cut the steerer down, not recommended until you have your right fit.

Hope this makes some sense.