The purpose of the study is to learn about the safety and effects of the study medicine (called ritlecitinib) for the treatment of alopecia areata. Alopecia areata is a disease that causes hair loss on the scalp, face, and areas of the body. Ritlecitinib is approved in many countries at a dose of 50 mg (milligram) taken by mouth once a day for the treatment of patients 12 years and older with severe alopecia areata. This study will look at both the 50 mg dose and a 100 mg dose. This study is seeking participants who: * Are 12 years of age or older * Have a diagnosis of alopecia areata * Have lost 50% or more of the hair on their scalp * Do not have any other conditions that causes hair loss * Are willing to stop all other treatments that they may be taking for alopecia areata About 550 participants will take part in in this study. Participants will be chosen by chance, like drawing names out of a hat, to receive 1 of 2 different amounts of ritlecitinib (50 mg and 100 mg) taken by mouth once daily. The 2 doses of ritlecitinib in this study will be compared to each other and also to data from previous studies. This will help to see if the 100 mg dose of ritlecitinib is safe and effective. People will be in this study for about 13 months. During the study, participants will need to visit the study site up to 9 times. Participants will undergo various tests and procedures such as: * alopecia areata assessment, * physical examinations, * hearing tests, * blood tests, * x-ray, * ECG (electrocardiogram), * photographs of the scalp and eyes. Participants will also be asked to complete questionnaires about their alopecia areata.