I have been imputing my password but it is saying verification failed that I can connect to ICloud

Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Restore - If you see an error when you update or restore your iPhone, iPad, or iPod

Backup - Restore your device from an iCloud or iTunes backup.      

Are you running any anti - virus programs? Using a VPN?

If the problem is still there, try booting into the Safe Mode using your normal account.  Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer or by using the developer’s uninstall instructions. For each disable/delete, you will need to restart if you don't do them all at once. 

Safe Mode - About.    

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin

https://etrecheck.com

This seems to be a common malady in the past few weeks? I have been online and on the phone with Apple Tech Support for over 3 hours over the past couple of days. My iPhone and iPads all work fine and I can log in to my apple id. On my MBPro its a no go. on the first call I lost all my safari pws and it wiped out my email pws. no access to iMessage or any other cloud from mbpro but ok from mobile. set up new user and apple id works fine... but not with my existing account. First notices said I was locked out after several wrong access attempts - they weren't the wrong pw at the time, but that I had to wait for notification from apple to try and log back in again - could be days they said. I tried again in a few days and was able to log into my apple id site (and obviously here) using the same pw as I tried to use in sys pref's to log into apple id... I have since upgraded to big sur as recommended but the update wiped out my site pws, and email pws again. log files have now been sent to a "higher level"... hope nobody else is going through this ****!

btw... been an apple user since 1981 and never had this inability to trouble shoot with its subsequent problems. support os trying but it seems they haven't been armed with the complete set of pages to follow to ensure we are not blowing up our files

I still cannot login, is there any bugs on apple server side ?

https://discussions.apple.com/thread/252778332

Everything is showing that it is working.

Apple - Support - System Status

I have same problem.

If you find a solution, share with us the solution please.

Thank you.

I out my password in and then it tells me that vertification failed. What am I doing wrong.

Did you try what I posted above?