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 input the values in the custom field.
In Issue View mode, the user have permission view or edit will see the value of the custom field.
Click on this custom field to go Edit mode.
If user don’t have permission
Field Security Group Picker get the value from the chosen custom field on Issue. The application will process the value.