Hello bigalwood,
Welcome to Apple Support Communities. I understand that you’re repeatedly being prompted to verify your Apple ID in System Preferences on your Mac. I’m happy to help.
Let’s start by restarting your Mac. Once you’ve fully restarted, are you still being prompted to verify your Apple ID?
If you’re still being prompted to verify your Apple ID, please sign out of your Apple ID using the steps here: Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support
Then, use the steps here t sign in to your Apple ID in the section titled “Sign in on your Mac” here: Sign in with your Apple ID - Apple Support
I also recommend checking for macOS updates. Apple has recently released a supplemental update to macOS Catalina.
Take care.