This "continue on" message seems to be a new message appearing in various contexts. If you are doing something where an app-specific password could be involved*, follow the steps in Sign in to apps with your Apple ID using app-specific passwords - Apple Support
How to generate an app-specific password
1. Sign in to appleid.apple.com.
2. In the Sign-In and Security section, select App-Specific Passwords.
3. Select Generate an app-specific password or select the Add button , then follow the steps on your screen.
4. Enter or paste the app-specific password into the password field of the app.
Others report having encountered this in various contexts such as when editing Apple Account information with a web browser. You can try proceeding editing the information as indicated in the messages by using Settings. Others have found using a different browser or simply trying again may work.
Related discussions:
https://discussions.apple.com/thread/255037783
- "Someone in another post said to use a different browser (not Safari or whichever one you normally use). That worked for me."
- "Use a computer to generate the App specific passwords. Don't use Safari or Chrome. I got it to work using Firefox on my Mac."
- "the Chrome browser works for me."
Can't change Apple ID - Apple Community
- "OK it just worked. No idea what was going on before. Thanks for the help anyway!"
Can't Change / Remove Apple ID Notificati… - Apple Community
- Occurred while changing account information using a web browser.
I can't find how to continue App Specific… - Apple Community
- "The solution to the problem is not to allow the iPhone or Mac to sign you in automatically with FaceID or TouchID, but instead I found complete success in manually signing in with my Apple ID and password, which then prompted a two-factor authentication prompt and code. Following that sequence, I was able to successfully revoke and add app-specific passwords."
https://discussions.apple.com/thread/255042597
- So I ended up getting on the phone with Apple about this… turns out it was an issue with Safari. As soon as I tried to create a new app-specific password in Chrome, it worked perfectly.
