Hello iConverted,
Thanks for posting in the Apple Support Communities. We're happy to look into this with you. We understand that you're unable to clear your Messages notifications on your iPad. Are these messages syncing to your iPad from another device? For example, are you having messages forwarded from an iPhone?
We see that you've listed iOS 9 as being installed on the iPad. What's the exact version of iOS 9 you're using? This is in Settings > General > About > Version. If you don't have iOS 9.3.6 installed, you may want to try updating to see if that corrects the issue.
Update your iPhone or iPad - Apple Support
Update your iPhone or iPad wirelessly
1. Back up your device using iCloud or your computer.
2. Plug your device into power and connect to the internet with Wi-Fi.
3. Go to Settings > General, then tap Software Update.
4. If you see more than one software update option available, choose the one that you want to install.
5. Tap Install Now. If you see Download and Install instead, tap it to download the update, enter your passcode, then tap Install Now. If you don't know your passcode, learn what to do.
Be sure to follow step #1 before updating the software. This will ensure that all your data is safeguarded and available for restore, should you need to recover it.
Best regards.