Dark region around my mole after i applied apple vinegar acid for 3 days?

Why?: Why did you do that? Vinegar is acetic acid, which is a relatively weak acid that can cause some chemical changes - it does not "cure" moles. Instead of fooling with your mole, get a dermatologist to remove it. That gives you a diagnosis and solves the problem. Obviously, if it wasn't bothering/worrying you, you would not be self treating.