iMessage varification message keeps popping up

Hi there The Lamb,

If you are still being prompted for your iMessage password whenever you open the Messages app, I would start by signing out of iMessage in the Settings:

Messages

1. Tap Settings > Messages.
2. Tap Send & Receive.
3. Tap your Apple ID, then tap Sign Out.

Sign in with a different Apple ID on your iPhone, iPad, or iPod touch

https://support.apple.com/en-us/HT203983

Once you do that quit the Settings and Messages apps:

Force an app to close in iOS
https://support.apple.com/en-us/HT201330

1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.

When you have done that restart the device, sign back into iMessage, and test the issue again:

iOS: Turning off and on (restarting) and resetting
http://support.apple.com/en-us/HT201559

Thank you for using Apple Support Communities.

I appreciate the update! The next step in the software troubleshooting would be to backup your device to iTunes, then restore it as new and verify that it works.

How to erase your iOS device and then set it up as a new device or restore it from backups
https://support.apple.com/en-us/HT204686

If it does work fine when restored as new, then restore your backup to either verify it still works and the software just needed reinstalled, or isolate the issue to the backup file itself if it starts happening again after you get your backup reinstalled.