We tend to use "whatsoever" to add emphasis to the end of a negative statement. For example:
There is no problem whatsoever.
That makes no sense whatsoever.
You could replace "whatsoever" with "at all" in these phrases, and the meaning would be the same.
"Whatever" is a conjunction meaning "anything or everything that". It's often followed by a noun+verb phrase. For example:
I'll do whatever you want.
He agrees with whatever she says.