You can Show/Hide the fields to portal users based on the condition match that is set and configured in the “Conditional Management” for the fields. (Portal Layout Settings -> Field Management)
When the portal user selects a Field, which is set as Conditional Field, the Field which is selected in “Visibility Field” will appear in add/edit of any objects.
Here, the “Status” field is selected as Conditional Fields and the New option is selected in the “Conditional Field Option”, by clicking on it, the portal users will get the Case Type which is set as a Visibility Field in the Field Management -> Conditional Management from the Salesforce CRM.