ASUS - ZenTalk

Hi hayyam
Thank you for your asking. Kindly provide the information below so that we can better assist you.
1. Your current firmware version
Settings>System>About Phone>Software information
2. Does the issue appear right after any system/apps' download or update?
3. Please try to enter "Safe Mode". If the SMS works well in Safe Mode yet the issue remains out of Safe Mode, please check on any disturbance from the installed 3rd party apps.
# How to enter and exit "Safe Mode"
https://www.asus.com/support/FAQ/1005163/
4. If the issue remains the same, please provide me the screenshot of your question and elaborate more about the situation.

Hi Christine
Here is my FIRMWARE version (attached)
2. Does the issue appear right after any system/apps' download or update? NOPE...THIS ISSUE WAS HERE FROM THE BEGINNING..
SMS now is came right now...It is OK
But Outlook (version 4.2039.4) not counting badge
Please look attached image. There is NEW MAILS in Outlook but no BADGE notification?
Also look Otlook App Notification settings

Hi hayyam
Thank you for your reply. I can duplicate the same situation on my phone, too. Because it is a single app issue, kindly report to the app developer, Outlook, for further assistance. Sorry for any inconvenience it may be caused. 
If you face the issue for other apps, please check
long press Home screen>Preferences>Unread counts badge>App list, make sure to tick all the preferred apps in the checklist