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Each resource that supports custom fields (incident, scriptrun, requirement, script) has an optional expand called "FieldValues". FieldValues is an object with properties for each custom field and values representing the values for that type of custom field.
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When you PUT picklist values - only the Id is required. This is the Id of the pick list value. The list of Id's Ids for picklist values can be retrieved via the customfield/{name}?$expand=Options resource.
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