Apple ID password verification failed

My iPhone and iPad keep asking me to re-enter my Apple ID password which I know is correct. When I re-enter it a get a notification that the verification failed and in smaller print it says this application does not exist. I do not even know what that means. I even CHANGED my password TWICE to make sure it was correct. It still did not work. I turned off my WIFI and only used my cellular data and it still didn’t work. Can someone please explain what I should do other than change my password and use cellular data. Is this a problem that happens frequently?