The most well known of the coxsackievirus infections is hand-foot-mouth disease âusually caused by coxsackievirus A16. Several other coxsackievirus infections are quite common. Most of them sometimes come with a rash or exanthem.he most well known of the coxsackievirus infections is hand-foot-mouth disease âusually caused by coxsackievirus A16. Several other coxsackievirus infections are quite common. Most of them sometimes come with a rash or exanthem.