Like in Germany where fascism rose as an alternative to the growing communist movement. The broader question I'm asking is are communistic/socialistic movements and fascist movements generally paired (as also seen currently with Bernie and Trump)
Communist rule over the USSR prevented any Fascist groups from developing in the 20's and 30's.
That being said, there were groups that would probably fit the later definition of Fascism active in late Tsarist Russia. Most notable of these were the "Black Hundreds", which were ultra-religious anti-semitic anti-communist nationalists and conducted various pogroms throughout the early 1900's. These groups were annihilated by the Bolsheviks, though.
During the war itself, the nature of the German invasion (i.e. wholesale slaughter and repression of the locals) prevented much popular support and the formation of an effective anti-Bolshevik Fascist army. There were various pro-German Russian groups (the National Liberation Army, Committee for the Liberation of the Peoples of Russia, etc.) but these were small, marginalized, distrusted by the Germans themselves, and less Fascist than simply anti-Stalinist.
During the 1920s and 1930s there were some fascist groups formed by Russian emigres in north eastern China. This includes Konstantin Rodzaevsky who formed the Russian Fascist Party, and Nikolay Ustryalov who outlined an ideology of 'National Bolshevism'.
Ustryalov saw the USSR as essentially only communist in appearance, and that at its core it was 'white'. Ustrayalov was able to return to the USSR in 1935... then got purged in 1937. Rodzaevsky collaborated with the Japanese occupation forces, and was arrested in 1945 and eventually executed.
"The Beast Reawakens" by Martin Lee discusses Ustryalov a bit as I recall but it has been some years since I read it.