can you send and receive new emails?
Or do you just see the old ones.
That would mean that your password is incorrect and it will spam you with that notification.
also, if you're using a different app then the built in one I would suggest uninstalling the app and reinstalling.
Keep us updated!
Which email you are using? It could be someone else trying so be aware of that.
In hotmail/outlook you can check your recent activity.
You can always change your security alerts setting to let those alerts go to an email you are not using frequently hence less annoying. Though I wouldn't recommend doing that!