OK, thanks for the additional information.
You could try the following:
-Quit the Mail app
-In > System Preferences... > Internet Accounts, click on that account to select it
-Change the password to something else and press Enter/Return
-It will spin for a while, then return an error that it is Unable to verify account or password.
-Enter the correct password and press Enter/Return
-If it accepts it without error, quit System Preferences and try the Mail app to see if the issue is resolved
Let us know if that fixes it,
C