A specialty pediatrician must finish high school and then does: 1  4 years of college. 2  4 years of medical school. 3  3 years of general pediatric training in a hospitals.4  1 &endash;3 years (usually) of special pediatric training (called a subspecialty). 4 years of college. 2  4 years of medical school. 3  3 years of general pediatric training in a hospitals. 4  1 &endash;3 years (usually) of special pediatric training (called a subspecialty).