Messages showing "new messages" incorrectly

You may try some of these steps, please check after each step....

1. If you have multiple devices, messages are being read on those devices, but on this specific device, the notification badge still shows unread messages due to a lack of internet connectivity.
2. Sometimes, a simple restart can resolve temporary software glitches. Turn off your iPhone, wait for a few seconds, and then turn it back on.
   1. Restart the device. That's it.
   2. Still not solved --> Force restart iPhone - Apple Support
3. If the issue persists, you can try resetting all settings on your iPhone. This will not erase your data but will reset all personalized settings to their default values. Go to Settings > General > Transfer & Reset > Reset > Reset All Settings and confirm the action. Note that you will need to reconfigure your settings afterward. All settings—including network settings, the keyboard dictionary, the Home screen layout, location settings, privacy settings, and Apple Pay cards—are removed or reset to their defaults. No data or media are deleted.
   1. Reset All Settings: Return iPhone settings to their defaults - Apple Support:- Return iPhone settings to their defaults
   2. You can return settings to their defaults without erasing your content.
   3. If you want to save your settings, back up your iPhone before returning them to their defaults. For example, if you’re trying to solve a problem but returning settings to their defaults doesn’t help, you might want to restore your previous settings from a backup.
4. Make sure you have the latest updates installed.
   1. Update Over-the-Air (OTA) —> Update your iPhone or iPad - Apple Support (IN)
   2. Update using iTunes/Finder —> Update your iPhone, iPad, or iPod touch - Apple Support (IN)