Introduced in Blood and Chrome. Very similar to the Mk II so I didn't spot it at first. The fuselage seems more bulky, the cockpit canopy seems more rounded and the wings slightly larger.
Didn't think we'd see anything else but I thought this was a nice easter egg considering it'll probably be the last BSG we'll see for a while.
Does raise the question why Mk IIs are still being used in Razor...
Bunch of possible reasons: attrition, airframe fatigue, not enough IIIs to go to all squadrons. Real world, we had two squadrons of A-7s still flying in the Gulf even though the Hornet had entered service 8 years early. More recently, Navy/Marine F/A-18 squadrons have switched from C models to A+ because the Alpha+ had more airframe life than the charlie stockpile. Plus, newer pilots tend to get older gear.
Something slightly older - look at Spitfires. By 1944 squadrons were re-equipping with the Griffon engined Mk XIV, but until the end of the war the older Mk IX was still considered a very good fighter. In fact many Mk Vs continued in secondary roles on the front line.
Or for the Americans, the P-51, where P-51B and P-51D variants, despite fairly significant differences, stayed in service until VE-Day, and the later K model as well.
So, especially considering the nature of the war, Mk II and Mk III Vipers probably served alongside each other, Galactica is very new in B&C so probably left dock with a wing of new fighters on board. The majority of the fleet would continue to use Mk IIs, or even Mk Is.