How can I increment the badge counter each time a push notification is received (iOS/REST API)?
iOS device does not increment the badge counter automatically each time a new push message is received. To manage badge counter you need to send push notification with proper badge value.
Please refer to http://quickblox.com/developers/SimpleSample-messages_users-ios#Universal_push_notifications
There is also a possibility to send push and manage badge value from Admin panel.