This is a shortened contraction of Shouldn't and Should Not. It usually is used by those with a southern-like accent or anyone making an accent on the words.
Tanor: Hey, UMG blocked meh from seeing this video. It says tis not available in my country. But why? I'm from the US. I shon't be having this problem! =(
Dash: You might have to renew yer internets...
Tanor: Aww man.
Should but won't do something
I shon't help you find your phone