Notification on new app version in IOS app store
No, there's no way to do this from the App Store.  Developers do not have access to any Apple API to notify users when a new version is available within the App Store.  

Developers can notify users within their own app that a new version is available.  For example, I have several apps that send me a popup message about a new version but I must open an older version of that app first, before I can see the notification.