To display a custom attribute on the category edit page in the Magento admin panel, a developer should use the UI component approach. This involves creating a category_form.xml file within the view/adminhtml/ui_component directory of the module. This XML file defines the form fields (including any custom attributes) that should appear on the category edit page. The UI component system in Magento provides a flexible way to manage form elements and their interactions on the admin side, ensuring a consistent user interface and experience.