What I was looking for here, was quarter ton models that were developed from an earlier civilian model.
The CJ-3A was modified to become the M38 (Willys MC) and the CJ-V-35/U.
The CJ-3B was modified to become the M606. (Forest Whitaker drives an M606 in Good Morning Vietnam!)
The CJ-5 was modified to become M606A1 (12 volt electrical system) and M606A2 (24 volt).
The J8 is a modified JK Wrangler built in Chrysler's Cairo plant.
But since some of the answers strayed from the "quarter ton" criteria, let's cover some of the other models.
FSJ/Gladiator pickups became M715 5/4 ton trucks, M725 Ambulances, and M726 Shop Vans.
FC-170 Forward Control pickups became the M676, M677, M678, and M679 cargo, van, and ambulance bodied military trucks. None of these were based on the shorter wheelbase FC-150.
While it is certainly true that nearly every vehicle (car and truck) can get accepted at some point for military evaluation, I doubt you will find evidence that any Jeepster (VJ, VJ-2, VJ-3, C101, and C104) was commonly used in military service.
And I guess if we consider that the CJ-10 is a civilian model truck, then the CJ-10A Air Force tug is a military vehicle developed from that truck.