The purpose of this study is to learn about the effect of a study medicine called rimegepant in adolescents who have frequent migraine attacks. Rimegepant is a tablet that dissolves when you put it on or under your tongue. The study will enroll participants who have headache for 15 days (or more) every month, of which 8 days (or more) of migraine every month, and each untreated attack lasts for an average of 4-72 hours In the 1st part of the study approximately half of the participants will receive a rimegepant tablet every other day, and approximately half of the participants will receive an inactive oral tablet (that looks the same as the rimegepant tablet) every other day. Participant experiences when they are taking the study medicine will be compared to when they are taking the inactive tablet. This will help to determine if the study medicine is safe and effective. The 1st phase of the study will last 3 months. In the 2nd part of the study all the participants who stay on study will receive rimegepant tablet every other day. This 2nd phase of the study will last 1 year. This will help determine if the study medicine is safe when taken for a long period. Those who will participate in both phases will have up to 19 visits at the study clinic, about one every 4 weeks (this may vary from 2 to 8 weeks interval during the study). Home health visits may occur as well. A health check and blood sample will be conducted at all visits. Participants will have to complete a daily diary to record the migraine attacks.