Prompting for wrong Apple ID while signed into correct one

The situation you describe can happen if there are apps (or media purchases) on the device that were installed (or downloaded) under a different Apple ID/account, and they need updating or redownloading. This can sometimes happen if a device was not properly reset by a previous owner, or if you incorrectly "change" your ID by creating a brand new Apple account instead of as in: Change your Apple ID - Apple Support

The best way to resolve this is to delete the item(s) requesting the update, and then download it again using the Apple ID that is signed in with the device.

You want to be careful that you do not lose any data, so be sure to check with the app developer to determine if removing the app will cause data loss.

These steps from "Delete apps on your iPhone, iPad, and iPod touch" [at: How to delete apps - Apple Support ] will help you remove the app:

How to delete an app

1. Touch and hold the app.

2. Tap Remove App [the "-" icon]. Remove App is the third option in the menu.

3. Tap Delete App, then tap Delete to confirm.

Keep in mind that some built-in Apple apps can't be deleted from your device, so you might not see the option to delete an app. Here’s a list of built-in Apple apps you can delete from your device [at: Delete built-in Apple apps from your iPhone, iPad, or Apple Watch - Apple Support ]. If you can't delete an app that's not made by Apple, disable parental controls [see: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support ], then try deleting the app again.

If you touch and hold an app from the Home Screen and the apps start to jiggle:

1. Tap the Remove icon in the upper-left corner of the app. (There's also an Add button in the top left corner of the screen and a Done button in the top right corner of the screen.)

2. Tap Delete App, then tap Delete to confirm.

3. Tap Done.

Once deleted, adding the app using the correct Apple ID should resolve the issue. See the article: Download apps and games on your iPhone or iPad [ Download apps and games on your iPhone or iPad - Apple Support ]

If many paid apps are involved and you purchased them with an old account, an alternative is to share them with your new account using Family Sharing --> Set up Family Sharing - Apple Support

Check these. There are several likely places where you can use a different Apple ID:

1. In Mail if you want to use a different, or more than one, iCloud account. Settings -> mail -> accounts -> add account -> iCloud

2. Messages and Facetime. Sign into a different Apple ID for these services in Settings. Note this has to be the same ID for both. Go to Settings > Messages > Send & Receive, and make sure both your telephone number and Apple ID are input there and both show a checkmark. If you need more help, check this link: Add or remove your phone number in Messages or FaceTime - Apple Support .

3. In the support article: If you subscribe to Apple One and use a different Apple ID for iCloud - Apple Support Apple alludes to using a different Apple ID for media, subscriptions, and purchases, but doesn't describe how to do this.

In iOS/iPadOS: Go to Settings > [your Apple ID] > Media & Purchases. Sign out of the current ID and sign in with a different one.

In Ventura: First, quit Settings. Then, in App Store, choose “Sign Out” in the Store menu, then click on the “sign in” button that appears in the main window. You can then sign into the other account. (from: Using different Apple ID for media & … - Apple Community )

4. Use a different Apple ID to share purchases with Family Sharing as outlined in Use a different Apple ID to share purchases with Family Sharing - Apple Support