Hello @cliff.ching ,
No, we do not have that feature in the API to get the historical list of the case system ID and their submitted search fields linked to a specific group.
I advise you to use the WC UI to view all the cases related to a particular group by using filters available on the left hand side of your UI when you are in the case manager page. You can filter cases in the case manager page by choosing a specific group whose case you would like to view.
Thanks,
Irfan Khan