A Long-Term Study of Zasocitinib in Children and Teenagers With Plaque Psoriasis

Inclusion Criteria

• Participant has a diagnosis of chronic plaque psoriasis for greater than or equal to (>=) 6 months prior to the screening visit.
• Participant has stable plaque psoriasis defined as no significant flare or change in morphology (as assessed by the investigator) in psoriasis for >=6 months before screening.
• Participant has moderate-to-severe plaque psoriasis as defined by a Psoriasis Area and Severity Index (PASI) score >=12 and a Static Physician's Global Assessment (sPGA) score >=3 at screening and Day 1.
• Participant has plaque psoriasis covering >=10 percent (%) of total body surface area (BSA) at screening and Day 1.
• Participant must be a candidate for phototherapy or systemic therapy.
• Inclusion Criteria for Part A Cohort 1: The participant is male or female and aged 12 to less than (\<) 18 years, inclusive.
• Inclusion Criteria for Part A Cohort 2 and for Part B: The participant is male or female and aged 4 to \<12 years, inclusive.
• Inclusion Criteria for Part A Cohort 1: The participant must weigh >=40 kilograms (kg) at the time of screening.

Exclusion Criteria

• Participant has evidence of nonplaque psoriasis (erythrodermic, pustular, predominantly guttate psoriasis, predominantly inverse, or drug-induced psoriasis). If a participant meets criteria for inclusion based on typical plaque psoriasis presentation, a limited amount of inverse psoriasis is not exclusionary.
• Participant requires systemic treatment, other than nonsteroidal anti-inflammatory drugs (NSAIDs), during the trial period for an immune-related disease.
• Participant has concomitant comorbid skin condition that, in the opinion of the investigator, would interfere with the trial assessments.
• Participant has history of active TB infection, regardless of treatment status and has signs or symptoms of active TB or evidence of latent tuberculosis infection (LTBI).
• Participant has active herpes virus infection, including herpes zoster or herpes simplex 1 and 2 or a history of serious herpetic infection.
• Participant has a history of chronic or recurrent bacterial disease.
• Participant has a history of opportunistic infections (for example, Pneumocystis jirovecii pneumonia, histoplasmosis, coccidiomycosis).
• Participant has any clinically significant medical condition, evidence of an unstable clinical condition or vital signs/physical examination/laboratory/ECG abnormality that would, in the opinion of the investigator, put the participant at undue risk or interfere with interpretation of trial results.
• Participant has any previous exposure to zasocitinib (also known as TAK-279 or NDI-034858) or other TYK2 inhibitors or participated in any trial that included a tyrosine kinase 2 (TYK2) inhibitor, unless participant has documentation of posttrial unblinding that confirms the participant did not receive a TYK2 inhibitor.
• Participant is not up to date on all required vaccinations according to current immunization guidelines as noted by country-specific pediatric authorities.

Other protocol-defined inclusion/exclusion criteria apply.