The only problem is that the feature for fetch and notifications for sub-folders / favorited folders are no longer available in iOS 11.x.
This was available till 10.3.3.
As a result of which, now any mail received in a favorited folder other than Inbox, are not notified.
Now if you use any other mail app, they divulge login credentials. While if you use Apple mail, it does not give you notifications.
WHAT TO DO?