I agree, Administration > Screens >
You should see three screen types.
Create, Edit and View Issues
Click on one of these and you can then see the Field Tab. You can create other Tabs also. Between chosen tabs you can add, re-order (drag and drop) or remove fields from the view (note new people don't ever delete fields in JIRA without thinking as someone may be using them!)
I usually use tabs on screens to break up large lists of custom fields. Would that work for you?
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