Whatsoever means at all, and it makes a negative absolute. No evidence whatsoever, none whatsoever, nothing whatsoever to do with it.
It goes after the noun rather than before it, which is unusual in English, and it only works with a negative — no doubt whatsoever is fine, some doubt whatsoever is not. Whatever does the same job less emphatically.
1adverbwhatsoeverAt all, used to make a negative absolute.
“I have no idea whatsoever where I left my keys.”
whatsoever is an intensifier.
Middle English whatsoever, from what plus so plus ever, all three intensifying one another.
Middle English
whatsoever
English, today
whatsoever
From Middle English whatsoever. by surface analysis, what + so + -ever.
Etymology from Wiktionary, CC BY-SA