The purpose of this study is to learn about the safety and effects of the study medicine (called Ritlecitinib) for the possible treatment of hidradenitis suppurativa (HS). HS is a disease causing long lasting painful red skin lumps. This study is seeking participants who: * have moderate or severe HS * have previously received antibiotics for HS that did not help, or could not tolerate antibiotics Participants will be randomly (like a flip of coin) assigned to receive either the study medicine or a placebo (a pill that looks like the study medicine but does not contain any medicine). The study medicine or placebo will be taken by mouth once daily at home. For the first part of the study, participants will receive a loading (starting) dose. For the next part of the study, participants will receive a maintenance (ongoing) dose. Participants will take part in the study for about 24 weeks (about 6 months). There will be about 10 study clinic visits: a screening visit, Day 1, and then every 1, 2, or 4 weeks until week 16. At each visit, participants will report on their health and have tests such as physical exams, blood and urine tests, vital signs, chest X-rays, ECGs, hearing tests, and questionnaires. Participants will record when they take the study medicine and their HS symptoms every day in an eDiary on a mobile phone. The experiences of participants receiving the study medicine will be compared to those receiving placebo to help see if the study medicine is safe and effective.