Yes! Mussolini was an ardent Socialist and crafted Fascism as a reform of it. Left Wingers have massively distorted their political rivalry and redefined the entire political spectrum.
No! If Fascism is to the right of Socialism, even by a small margin, it becomes a right wing ideology.
It takes a mob making decisions over everyone else (direct democracy) to succumb to a big lie and place a fascist leader at their head. Its inherently a left leaning ideology to create such a mob and overly empower it to where it can strip the rights of others away for their own "collective good".
Fascism relies on ultra-nationalism which is DEFINITELY a right wing position.
This is a matter of definitions and people still can't get it right. Worrying.