What you’re experiencing appears to be a case of a partially linked or ghost Apple ID, where your old Yahoo email address is still associated with some Apple service or setting.
Even though you're signed into iCloud with your current Gmail-based Apple ID, Apple systems may still be trying to authenticate the old Yahoo ID if it was ever used for iCloud, iMessage, FaceTime, the App Store, or past purchases. This often results in persistent pop-up prompts requesting the password for the outdated email address.
To fix this, start by checking all your Apple devices for signs of the old account. On any iPhone, iPad, or Mac you're signed into, go to Settings > [Your Name] > Media & Purchases > View Account and also check in Settings > Messages, FaceTime, Mail, or Passwords & Accounts to see if the Yahoo address is listed anywhere. If it is, remove it from each app or section where it appears.
Next, go to https://appleid.apple.com, sign in with your current Apple ID, and check under Sign-In & Security for any traces of the Yahoo account, such as being listed under Account Recovery Contacts or Trusted Numbers or Emails. If the Yahoo address appears, remove it from those sections.
If you're only seeing the pop-up while using a web browser, the issue could be a cached login session or an autofill entry trying to sign in with the old account. Try clearing your browser’s cookies and cache, or log in using a different browser or a private/incognito window to see if the problem persists.
Occasionally, iCloud.com may request login credentials for an old Apple ID because it's trying to sync shared data (like Notes or Find My) that was once tied to that account. If any of your devices still have remnants of the old ID signed in to background services, iCloud will keep asking for credentials until all traces are removed.
If none of these steps resolve the issue, it's likely that the Yahoo-based Apple ID is still linked to an old purchase or activation lock, and only Apple can fully remove it. In that case, it's best to contact Apple Support directly at Contact - Official Apple Support, explain the situation, and ask for help in removing or unlinking the Yahoo address.