In your project, add your custom field to the View screen. This way, the field's value will be visible if a value is set.
On the Edit screen, do not include the field.
On the Create screen, only include the field if you want issue creators to set this value.
Want only certain users to edit the field? One option is to include the custom field on a transition screen, and set a condition on the transition so only a certain role/group/user may access the transition.
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