"I do not know anything about him."
Translation:Ich weiß nichts über ihn.
über takes accusative when the meaning is 'about'. if you use dative, the meaning is 'over' and that would mean that you don't know anything what is positioned above him.
"ich weiße" is actually a different verb. "weißen" is regular and it means "to paint white". It's not a very common word, though.
"Kennen" is used for expressing aquantience with something. "Wissen" is used for expressing knowledge of something. Since this sentence expresses lack of knowledge about a man rather than the man himself, "wissen" should be used.
E.g.: "Ich kenne ihn nicht" means I am not aquatinted with him. "Ich weiß über ihn nichts" means i don't know anything specifically about him
I try to associate "wissen" with wisdom to help me make this distinction.