By the text 'Report category(public) created from CaseManger portal is comes into shared category by Default. But, i verified this in pega which is not true(creating in standard)', are you referring to any lesson in Pega Academy course. If yes, kindly point out the course name, lesson number, etc..
Also, mention the product version referred for above observation. This is because, from below post (of Pega 7.2.1), I see that report category is either public or private.
Further to my previous post, find below information regarding report categories:
"There are two types of Report categories—Private and Public (with standard and shared types). Private Categories are specific to an operator, so the reports in that category can be accessed only by that operator. Public Categories include all standard and shared reports.
There are two types of standard reports—reports that are shipped with the product and categories created by developers. When a developer creates a category, in this example ADV reports, it’s accessible for all users who can view the report browser.
Public Categories also include shared reports. When a manager creates a new category, PRPC saves it as a shared category and only users belonging to the same access group can access the reports in it. The Category is saved as a rule but when we open the rule we can see that it only has a short description. The category rule does not indicate the category type—Public (Shared or Standard) or Private (Personal)."
Refer the Reporting module of Senior System Architect course(7.1) from Pega Academy.