Well, the one that has flying reindeer pulling his sleigh not only lacks concrete evidence/logic of existing but also has history showing that he was deliberately made up.

However, Saint Nicholas who he was partially based on was a real person as far as anyone can tell.

The thing about a lot of deities is that the attributes to them can be as vague or inscrutable as one likes to avoid having to give proof of their existence. Like when people say, "God works in mysterious ways," to get away with saying God is all-good even in the face of tragedy.