Apple ID & Password issues

Did you signed out from location system preferences - iCloud and then signed with new Apple ID and password , was this id was set up as secondary authentication or two factor authentication , are your first owner of the Mac or did you purchased from some one else ?

If you'r Apple ID and password is not recognised there could be many reasons if the Mac user change date and time settings in the location , system preferences - date and time , also the location settings are altered , if you change read and write permissions in home folder , guest , shared folder .

Or some times system files get corrupted using unknown softwares , third party apps that are not compatible with Mac , some cleaners , antivirus ...

Secondary authentication is created using Apple ID and security questions and answers , two factor authentication is created by entering in appleid.apple.com with your Apple ID and password and security questions then turning on 2FA , you have to save trusted numbers ( it could be your land line number or a mobile number ) and whenever you sign with Apple ID and password a verification code appears on the mobile after filling up the credentials you can enter Apple ID account and that is secured method ) .

See some articles Get help with iCloud - Apple Support

iCloud: Trouble signing in to iCloud.com

uninstall those third party apps use https://etrecheck.com/

And post back the results .

If you didn't sign out of iCloud, what indications are you getting that it doesn't recognize your Apple ID and password?

You are welcome. Are you still getting the notification? There may have been a server error.