A Study of Zasocitinib in Adults With Hidradenitis Suppurativa

Inclusion Criteria: Participant Willingness: 1. Participant is willing and able to understand and fully comply with all trial procedures and requirements (including the use of digital tools and applications), in the opinion of the investigator. 2. Participant has provided written informed consent and any required privacy authorization before the initiation of any trial procedures. Disease Characteristics: 3. Participants must have signs and symptoms of hidradenitis suppurativa (HS) for at least 6 months prior to screening, and a diagnosis of HS (confirmed by a dermatologist) at the screening visit with stable HS signs and symptoms for 2 months before screening, as determined by the investigator through interview or medical history. 4. Participants should have HS lesions in at least 2 distinct anatomical areas, one of which must be at least Hurley Stage II or III at both screening and Day 1. 5. Participants must have a total of greater than or equal to (\>=) 5 inflammatory lesions (that is, number of abscesses plus number of inflammatory nodules) at both screening and Day 1. 6. Participants must have a history of inadequate response to a previous course of oral antibiotic for treatment of HS or exhibited recurrence, intolerance, or contraindication during that course of oral antibiotic, as assessed by the principal investigator. Age and Reproductive Status: 7. Participant is aged \>=18 years at the time of consent. In the European Union (EU)/European Economic Area (EEA), for participants aged 65 years or older, the investigator must document a favorable benefit-risk assessment to justify the participant's inclusion in the trial. 8. Participant meets the following birth control requirement: 1. An individual with potential for pregnancy, who is now surgically sterile; OR 2. An individual of nonchildbearing potential with laboratory confirmation of postmenopausal status; OR 3. If sexually active with a nonsterilized individual who produces sperm, an individual with potential for pregnancy who agrees to use a highly effective method of contraception from the signing of informed consent throughout the duration of the trial. The use of effective contraception will be required for participants assigned male sex at birth. In the EU/EEA, for participants who elect to use hormonal contraception as a form of highly effective contraception, the investigator must document a favorable benefit-risk assessment to justify the participant's inclusion in the trial at screening and every 3 months during the trial. 9. For participants in the EU/EEA, the investigator must have no reason to believe that the participant would be placed at risk by participating in the trial with regard to the European Commission decision as of 10 March 2023 on measures to minimize risk of serious side effects with JAK inhibitors (EMA/142279/2023) and the UK Medicines and Healthcare products Regulatory Agency (MHRA) guideline on Janus kinase (JAK) inhibitors: new measures to reduce risks of major cardiovascular events, malignancy, venous thromboembolism, serious infections and increased mortality as of 26 April 2023. Exclusion Criteria: Target Disease-Related Exclusions: 1. Participant has a draining tunnel count of greater than (\>) 20 at screening or Day 1. 2. Participant has any other active skin disease or condition (for example, bacterial cellulitis, Candida intertrigo, extensive condyloma) that may, in the opinion of the investigator, interfere with the assessment of HS or participant has developed a concomitant comorbid skin condition that, in the opinion of the investigator, would interfere with the trial assessments. 3. Participant has a diagnosis of sarcoidosis, systemic lupus erythematosus, or active inflammatory bowel disease. 4. Participant has a diagnosis of inflammatory conditions other than HS, including but not limited to, psoriasis, psoriatic arthritis, and rheumatoid arthritis. Recent/Concurrent Infectious Disease Exclusions: 5. Tuberculosis (TB): 1. Participants have a history of active TB infection, regardless of treatment status. 2. Participants have signs or symptoms of active TB (including, but not limited to, chronic fever, chronic productive cough, night sweats, or weight loss) as judged by the investigator. 3. Participants have evidence of latent tuberculosis infection (LTBI) as evidenced by a positive QuantiFERON (QFT) result OR 2 indeterminate QFT results, and participant does not have documentation of appropriate LTBI prophylaxis or is not able or not willing to initiate appropriate LTBI prophylaxis. Participant remains eligible if there are no signs/symptoms of active TB AND documentation of no history of active TB can be provided AND (1) participant can provide documentation of prior and complete treatment for LTBI (appropriate in duration and type per current local country guidelines) or (2) participant has a positive QFT result or 2 indeterminate QFT results but has initiated prophylaxis (appropriate in duration and type per current local guidelines) a minimum of 2 weeks prior to Day 1. In the EU/EEA, participants with evidence of LTBI, regardless of prophylaxis treatment status, must receive approval to participate in the trial from an infectious disease or other TB specialist (for example, pulmonologist). Note: TB prophylaxis regimens should be administered according to local guidelines; however, because of potential interactions with zasocitinib, rifampin should not be used. For isoniazid monotherapy, a minimum of 6 months should be used. TB testing should be conducted using QFT-TB Gold submitted to the central laboratory unless alternate or additional tests are required per local guidelines. 4. Participant has had any imaging trial during or 6 months prior to screening, including x-ray, chest computed tomography, magnetic resonance imaging, or other chest imaging suggesting evidence of current active or a history of active TB. X-ray is req