The Luftwaffe Field Divisions were the ground forces of the Luftwaffe. They were created in 1942 to help alleviate manpower shortages of the army as well as for Hermann Goring to have his own prestigious soldiers as opposed to the army.
They would be a Riflemen squad. Their unique weapon could be the Selbstlader M1916 carbine. The Selbstlader M1916 was an early semi-automatic rifle used in WW1. In its original full rifle form it performed well in tests but was rejected because it was too delicate for the horrible muddy conditions of the war. However it had potential up in the air as you don’t have to worry about mud or dirt or debris in the sky; and it was adopted by the German airforce. Plane warfare was still in its infancy and aircraft machine guns were not fully developed yet so early plane crews would literally shoot at their targets with rifles. The original Selbstlader M1916 rifles were pressed into air service, but a shorter carbine variant (the one I think should be this squad’s unique weapon) was made and was the most common and produced form of this rifle. (On a separate note perhaps the original long rifle Selbstlader M1916 could be a gold order or event weapon)
Would have happened eventually as allies gained air superiority