As an armchair tactician it seems that a paratrooper attack would negate the distance the German army had to drive to reach Moscow and would be able to cut off the retreating red army in the first year of the war on the eastern front. was there ever any invasion plans that included an airdrop of the Fallschirmjäger in the Soviet Union. If not why weren't they used as airborne troops during the invasion.
Barbarossa was unlike earlier German campaigns in the war in that there were no major air landings or airdrops. There were some very small-scale airdrops during the opening phases of Barbarossa, but these were nothing like the Fallschirmjäger operations in Scandinavia, the Low Countries, and the Balkans. The VII Flieger-Divison and some Fallschirmjäger regiments were also employed on the Leningrad front late in the campaign, but they operated as a ground-only units. This distinct lack of paratroops in the campaign can be traced to two interrelated causes.
The first and most obvious reason was the massive losses the Fallschirmjäger incurred in the invasion of Crete. Although successful, Merkur ripped the guts out of Kurt Student's expanded parachute corps. The invasion exposed real problems in German parachute doctrine, equipment, and tactics. Earlier airdrops also had high losses, but the victory at Crete was Pyrrhic. Much of the Fallschirmjäger units had to spend most of Barbaorssa reconstituting themselves. Additionally, these losses made German planners increasingly doubtful about the efficacy of mass airborne assaults. Hitler had conceived of using an airborne assault as a component of 1942's drive into the Caucasus, but German planners thought it not worth the effort.
The other reason for the lack of Fallschirmjäger airborne operations in the USSR was the Germans were starting to come up quite short on transport aircraft. Here Merkur too extracted a high price on Ju-52s and the Luftwaffe's transport aim had been hemorrhaging pilots and planes from the start of the war. These losses were beginning to outstrip replacements as early as 1941. To make matters worse, the latter stages of Barbarossa became more reliant on airdropped supplies as the Axis forces overstretched their logistical networks. Resupply by air became one of the means that isolated German units such as those in the Demyansk Pocket were able to fight on in through the winter campaign. The Luftwaffe kept up this logistical resupply by stripping training units of both aircraft and their instructors. This may have worked over the short-term, but this fatally damaged the long-term viability of the transport arm. Things were bad for the transport arm in 1942 and the Stalingrad airlift made matters exponentially worse.
This lack of aircraft meant that even when the Fallschirmjäger made good their losses from Crete, they lacked the aircraft to drop them. While some of the Luftwaffe's and Heer's air divisions would see action in the USSR, they were employed as ground-based infantry rather than as paratroopers.