Neither option is really incorrect from a grammar standpoint but a native speaker would not use either of them. We don't say that someone "hits on someone's face." On is used more when your face (or other part of your body) hits some inanimate object, like "I smacked my face on the open cabinet door" or in your example "I hit my knee on the table."
Instead we use "with" to indicate the object used to hit your face:
Best Answer
I'd call that a pinch. You can be more specific and say "she pinched his cheek", which means exactly what's shown in the picture.