Only users who have Edit permission can input the values.
On the Issue Screen, Jira has two modes ( Issue Create, Issue View).
In Issue Create mode, Edit permission is required. The users can choose the values in the custom field.
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In Issue View mode, the user have permission view or edit will see the value of the custom field.
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Click on this custom field to go to Edit mode.
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If the users don’t have such permission:
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Field Security User Picker gets the value from the chosen custom field on the Issue. The application will process the value.