iCloud login fails on Catalina

If you delete both web mail account ( say gmail account ) and iCloud mail account from system preferences > internet accounts .

( a ) when you select web mail account and click on minus sign , it will prompt are you sure you want to delete the account ( 1 ) cancel ( 2 ) ok and you click on ok the account will be deleted .

( b ) And if you delete iCloud account ( 1 ) do you want to keep a copy of your iCloud data on this Mac before signing out ? 

Cancel , keep a copy , so click on keep a copy .

Do you want to keep a copy of your safari passwords on this Mac ? 

( 1) delete from Mac .

( 2 ) cancel 

( 3 ) keep on this Mac .

So , click on keep on this Mac .

It will prompt to enter Apple ID password to turn off find my Mac , so enter and click on continue .

Do you want to keep a copy of your iCloud data on this Mac before signing out ?

If you don’t keep a copy , your data will be removed from this Mac but will still be available on other devices using iCloud .

( a ) the box for iCloud Drive is checked ( b ) the box for contacts is checked .

Now , open apple mail application , choose a mail account provider and select google click on continue , enter your web mail address and password and click on next , check the boxes of mail , contacts , calendars , notes and click on done .

The gmail account has been set and mails will start downloading .

Open system preferences and click on iCloud , a pop up window will appear iCloud lets you access your music , photos , contacts , calendars and more on your devices , automatically .

Sign in with your Apple ID and click on next and enter your Apple ID password .

( a ) check the box of use iCloud for your documents and data

( b ) use find my Mac

( 1 ) back ( 2 ) next so click on next .

A pop up window will appear allow find my Mac to use the location of this Mac

( 1 ) not now ( 2 ) allow so click on allow .

You have to enter your Apple ID password to set up iCloud Keychain and click on ok .

A pop up window will appear to set up iCloud Keychain on this Mac , request approval from one of your devices using iCloud Keychain .

( 1 ) use code

( 2 ) cancel

( 3 ) request approval

So , click on use code .

Enter your iCloud security code and enter the iCloud verification code sent to your trusted mobile and click on ok .

After some time , the box for keychain in iCloud will get checked , also check the box of Siri and make sure back to my Mac is always unchecked .

So , both web mail account and iCloud account are configured .

Please clarify are you using secondary authentication account or two factor authentication on Mac os catalina 10.15.3 have you deleted only web mail account ( say using gmail services ) or iCloud account or both are deleted at the same time , in system preferences - internet accounts do you see empty accounts or is there any , please post back .

Some people have solved this by going to System Preferences/Internet Accounts, selecting an iCloud account there, and signing in. You need to repeat this for each iCloud account.

You are welcome. Have you tried clicking the + sign at the bottom and adding it back?