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Yes, but you are (mostly) in contradiction to the scholarship on this issue. Again, from the wiki (with citations):
Fascism's origins are complex and include many seemingly contradictory viewpoints, ultimately centered on a mythos of national rebirth from decadence.[44] Fascism was founded during World War I by Italian national syndicalists who drew upon both left-wing organizational tactics and right-wing political views.[65] Italian Fascism gravitated to the right in the early 1920s.[66] A major element of fascist ideology that has been deemed to be far right is its stated goal to promote the right of a supposedly superior people to dominate, while purging society of supposedly inferior elements.[67]
So Mussolini used left-wing organizational tactics (which I assume was appealing to the downtrodden proletariat), but right-wing political views. To argue that is a spawn of the left is, at best, incomplete. And in its manifestation, it was clearly right-wing. And still is to this day. It is not in any way socialist or left-wing. It is the views that define any "-ism", not so much the origin (necessarily).
Left-wing authoritarians are not fascists because their views do not align with fascists, even if both are authoritarian.
