I have a 5th gen iPad 9.7 inch running iOS 11.3 with a “ghost” notification for a message that does not exist. It was delivered to both my phone and tablet and for some reason didn’t clear the notification on the opposite device, after it was read. I tried turning on and off every setting for messages, notifications, I re-read every message, cleared all from the notification center, deleted old failed to send messages, restarted the app, restarted the device, hard reset the device, I tried messaging myself and opening them and then deleting them. I refuse to do a complete factory reset and restore my entire device over an issue as simple as this. That’s Apple’s easy fix for everything. Just wipe the whole thing. That’s so unrealistic to do as small issues like this come up almost weekly, and a complete restore is honestly a giant pain in the butt, and they should have fixes for bugs like this.
Anyway, what ended up working for me was, thankfully there was a software update for iOS 11.3.1 available and installing that somehow fixed the problem and cleared the notification. I doubt there was a fix for it in the update, it probably just coincidentally fixed it.
For anyone else having this issue with annoying badge app icon notifications that won’t go away, try checking to see if a software update is available and maybe it will fix it. I wasted two hours trying to get that annoying little thing to disappear.