Badger connectors are pretty specific to Badger & are M5 x 0.45 - it's unlikely that you're going to find an adapter anywhere else other than from an airbrush outlet.
If you plan to use the Badger hose, you will need something like this to connect to the TC-20's 1/8" BSP outlet;
Precision German Airbrush sell the above part here, about 1/2 way down the page (part no. 104683);
http://precisiongermanairbrush.com/accessories_harder.html
If you plan to do away with the Badger hose, your easiest option would be to get a 1/8" air hose with a quick connect fitted & get a quick connect tail for the Badger.