When you set up the iPhone at the Apple Store, did you restore from a previous backup?
If that was the case, then those apps would have attempted to download from that backup and ask for that Apple ID that was cancelled. Finding those apps are not always easy. I suggest checking in the App Store for updates that have not been updated and also deleting apps on your iPhone that you may no longer use or could have been downloaded by another user. You may also be able to identify apps on your Home Screen or in the App Library(by swiping all the way to the left) that appear greyed out as they would not have been completely installed.
Also make note if you are using a different Apple ID for Media & Purchases at Settings > [name on top] > iCloud > Media & Purchases. Usually it is the same, but some users do use a different ID for purchases.
The only other solution to the problem of apps installed by other users is to wipe your iPhone and set it up as new. You would not be able to restore from a backup, so you would need to make sure that you are using iCloud Photos and any other data, such as Contacts, is stored in iCloud. You can see what data is being stored in iCloud by going to Settings > [name on top] > iCloud. Of course this would depend on how much iCloud storage you have and if the data will fit into that amount. Once it is set up as new by not transferring any data and you use your Apple ID and Password, then that data will be restored to your phone. Any apps that you previously had would need to be redownloaded from the App Store, but you will not be charged again for them. The Apps will have a cloud symbol next to them in the App Store for you to redownload. Any apps that were not downloaded by you will not have that cloud symbol.
I can't think of any other reason why you would be getting a pop-up to provide a different Apple ID other than an app that was downloaded from another user. Wiping the device would be a last resort, so hopefully you will be able to identify the apps and delete them to eliminate the pop ups. If anyone else has another reason, hopefully they will chime in.