The "Continue on one of your devices" message is part of the implementation of the Passkey feature for iOS, iPad 16 and Ventura. It is currently only supported by certain web sites and apps, including Safari. The site or app is making a call to your trusted device(s) for you to authenticate from the device itself (using Face ID or Touch ID). However, the remote user implementation appears to be unclear at this stage and it is probably best employed by first setting up Passkeys on your devices as provided in Sign in with passkeys on iPhone - Apple Support
If you are having problems with this feature when using Safari then an alternative solution is to not use Safari for what it is you are trying to do. Use a different browser that does not have this feature in it. See this August 17, 2023 post by Community Specialist Chris_V89 at i followed the exact steps of the app spe… - Apple Community
"does this issue occur […] at the Apple ID website in Safari? If so, to help with troubleshooting the issue further, try testing the issue in another web browser, if possible."
Related discussions:
every time I tried to create an app-speci… - Apple Community
- "Someone in another post said to use a different browser (not Safari or whichever one you normally use). That worked for me."
- "Don't use Safari or Chrome. I got it to work using Firefox on my Mac."
- "the Chrome browser works for me."
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.
How do you create an app specific passwor… - Apple Community
Using Chrome did the trick for me.
Can't create app specific password - Apple Community
Wow-using chrome worked
