Fascism and National Socialism had a common trajectory they started as radical revolutionary nationalist movements using some left-wing tactics to achieve power.
When power was at hand they allied themselves with conservative nationalists because right-wingers are more stable when you have a whole country to govern.
When you don't have power, you should unite with the revolutionary elements of society, when you achieve power you should unite with the conservative elements of society.
So you can say Fascism/NS were left before the nationalist revolution and right after after the nationalist revolution this transition happened in different periods of time.
Third position politics isn't the left or right as you know it they are opposed to both communism and capitalism.