I've never seen a 3/8" hex bore sprocket, nor did I find one in a dozen web searches. I'm not really surprised, as the only 3/8" hex shafts I have seen have been on tools (e.g. drill bits) and intermediate gears in gearboxes, not on the output shafts. Most of the sprockets I have seen with less than 1/2" bore have been designed to fit directly on motor output shafts, and I have never noted a motor with a hex shaft.
If you want a 3/8" hex bore sprocket, the easiest route I can see is:
Purchase an
AM-0278 or
AM-0281, bore the hole out to 3/8", then use a 3/8" hex broach in an arbor press.
Edit: Sniped - and Cothron's second solution is simpler than mine.