App store keeps asking for my Apple ID and password repeatedly and will not let me download updates how do you clear or stop this?

I was having a similar problem with my wife's Mac, which was running macOS 10.11 (El Capitan). The problems started after we set up Family Sharing, including Purchase Sharing, which included all of the sign-out / sign-in work to get her system fully onto her Apple ID for the various Stores. There were four updates for Apple apps (iWork apps, iMovie) that just wouldn't download, and kept repeatedly asking for first my Apple ID authentication, and then (after some of the things below) her Apple ID authentication.

What didn't work:

• Rebooting
• Signing out of the App Store, rebooting, and signing back in
• Signing out in System Preferences, and then signing back in
• Entering any password

After reading this thread, I decided to give deleting-and-reinstalling a try. I did it first with Keynote and—success!

So, naturally, I deleted the other three apps, and started them on their re-installations.

Part way through—horror! Prompted again for _my_ Apple ID and password, not my wife's.

But this time the message was different, and I think it finally provided the real source of the problem. The prompt was that we needed to (re-) enter the security code for the credit card set up for the Family Sharing purchases.

So I entered my Apple ID and password, and then entered the credit card security code. No problems since.

I have no idea why the App Store got stuck just asking for passwords, without providing the real problem, or what made it finally ask for what it really wanted.

But if you're having this problem, worth doing a tour through your payment method and other items, to make sure that the Family Sharing purchase payment method is fully set up.

Welcome to the Apple Support Communities!
I understand you are having trouble updating apps on the Mac App Store. Is the issue only with these four updates? Are you able to download a free app from the Mac App Store?
The first thing I would suggest is to sign out of the Mac App Store, and restart your computer. This will establish a new connection to the internet.
Before clicking on the Mac App Store, visit the Apple ID page below and confirm that you are able to sign in with your Apple ID and password. While you are in your Apple ID account, check the billing section to make sure everything is up to date and there are no blank fields.
Change or remove your Apple ID payment information

If you want to check your payment information:

1. Sign in to your Apple ID account page.
2. In the Payment & Shipping section, click Edit Payment Information.
3. Change your payment information.
4. Click Save.

Now, open the Mac App Store and sign in with the same Apple ID and password you used earlier.
Click on the Purchases tab. Try updating only one application at a time.
If the issue persists you can delete the app from the Applications folder in Finder and redownload it.
Redownload music, movies, TV shows, apps, and books from the iTunes Store, iBooks Store, and App Store
Take care.