A considerable amount of users on Reddit have a strange issue of iCloud asking to verify password once or twice in a day. Digging a little deep in the matter, it is evident that the issue is usually faced after upgrading iOS version or after restoring through iTunes.
If you are one the annoyed users, then we have a fix that works and hopefully should help you as well. In case this trick does not work for you but you have been able to solve it with something different, then do share it in comments. For now, refer below for the fix that seems to be working.
How to Stop iOS Asking to “Verify iCloud Password” on iPhone or iPad
Step #1. Open the Settings app from your home screen → Look for iCloud and tap on it.
Step #2. Now scroll till the end of the list and tap on Sign Out.
Step #3. You'll get a warning pop-up; simply tap on Sign Out again.
Step #4. On the second pop-up, tap on “Delete from My iPhone“. On receiving third pop-up, tap on “Delete from My iPhone” again.
Step #5. If you have Find My iPhone enabled, you'll need to enter your iCloud Password and then tap Turn OFF.
Step #6. Now you have been signed out of iCloud. Force restart your iPhone or iPad by pressing Sleep/Wake button along with Home button until you see Apple logo.
Step #7. Once your iPhone or iPad has restarted, login to your iCloud account from Settings app.
This should have solved the issue.