Why do ADHD medications have the effect of someone "picking"their skin and how to stop?

Medication. Picking is a for of anxiety. Stimulant mendication can make anxiety worse. Talk to your doctor as he/she may decrease the dose or change medication.
Couple things... One, adhd has a high association with tic disorders, and many times the treatments can exacerbate, expose or better yet unmask the tics to a degree. Picking the skin can be one of those nervous type tics that hyperactive people exhibit (or nail or cuticle biting, etc). Second, , many of the adhd meds are stimulants, same general class as caffeine or nicotine, and stimulants may stimulate tics.