Since Apple use Two-factor authentication as the security solution for your Apple ID and Apple device. When you sign in to a new Apple device or browser with your Apple ID, you need input a verification code to trust this device or browser. The verification code is a temporary code sent to your trusted device or phone number by Apple. It means that you can not receive this code when your other trust device is not around. So many users wants to stop the two-factor authentication notifications, but it doesn't work. How to fix?
To stop the two-factor authentication notifications from continuously popping up on your iPhone or other device, you need turn off this feature on the Apple ID account. However, not all Apple ID account can turn off the two-factor authentication.
New Apple ID account can't turn off two-factor authentication
You can't turn off two-factor authentication for some accounts created in iOS 10.3 or macOS Sierra 10.12.4 and later. If you created your Apple ID in an earlier version of iOS or macOS, you can turn off two-factor authentication. Apple documentation has a specific description about this. https://support.apple.com/en-us/HT204915
Turn off two-factor authentication on Apple ID account page
To turn off two-factor authentication, sign in to your Apple ID account page and click Edit in the Security section. Then click Turn Off Two-Factor Authentication. After you create new security questions and verify your date of birth, two-factor authentication will be turned off. If you don't see the option to turn off two-factor authentication on your Apple ID account page, that means you can't turn it off.
Turn off two-factor authentication on your mac with OS X EI Capitan or later
1. Go to Apple (?) menu > System Preferences > iCloud > Account Details > Security.
2. Disabled the two-factor authentication and set up the three security questions.
Turn off two-factor authentication on your my iPhone or iPad device
1. Go to Settings > Tap your name (Apple ID, iCloud, iTunes & App Store) > Password & Security > Turn off Two-Factor Authentication
If the two-factor authentication notification still showed up on your iPhone
If you already turned this two-factor authentication off on your apple id account, but it still keeps popping up notifications. You need sign out Apple ID and sign back again.
1. Go to Settings > Tap your name (Apple ID, iCloud, iTunes & App Store)
2. On this screen if you scroll to the bottom you'll see a Sign Out option. Click Sign Out.
3. Once you sign out, and you can go back into Settings and sign back into your account.
What if you can't access to a trusted device or didn't receive a verification code?
If you're signing in and dont have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number.
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