Q: my macbook pro keeps on asking for my apple id every time I use the cloud. I enter it and it asks again an so on. No bother on ipad or phone

In the iCloud pane of System Preferences, please uncheck the box marked Mail and check it again.

Please back up all data before proceeding.

Triple-click anywhere in the line below on this page to select it:

~/Library/Caches/com.apple.iCloudHelper

Right-click or control-click the line and select

          Services ▹ Reveal in Finder (or just Reveal)

from the contextual menu.* A folder should open with an item selected. Quit the application if it's running. Move the selected item to the Trash. Relaunch the application and test.

*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combination  command-C. In the Finder, select

          Go ▹ Go to Folder...

from the menu bar and paste into the box that opens by pressing command-V. You may not see what you pasted because a line break is included. Press return.

Did this start happening when you set up two-factor authentication? What is the exact, complete text of the password prompts?

I think you may have enabled two-step verification. Please take the steps in the article linked below. If you can't take those steps, or they don't work, click the Support link at the top of this page to contact Apple Support. Select "Apple ID" as the product you need help with and you may avoid being charged the support fee.

Frequently asked questions about two-step verification for Apple ID - Apple Support

Please update this discussion with the results of your contact with Apple, so that others can benefit from your experience.

Thanks for the update.