"Sign In To iTunes Store" messages for Apple IDs that aren't mine

None of those other Apple IDs are mine though, so there wouldn't be any apps I would have purchased using them. I just checked the iTunes and Apple Store section of my iPhone and I only see one Apple ID listed there so I can't see where I'd be able to figure out if there were any other apps that somehow came from some other apple ID.

I don't see how that is possible. The Purchases History doesn't list which Apple ID bought it because purchases are grouped by Apple ID. In other words, I have to click on my Apple ID and provide my passcode before I can even see my purchases list. And there are no other Apple IDs available to me from that iTunes & App Store settings screen of my phone.

I looked through all the apps on my phone and I know that I downloaded or purchased each of them. I deleted some older ones I haven't used in a long time just in case, but the problem persists. Moreover, there would have to be 8 or 9 apps that were linked to someone else's account, since there are 8 or 9 consecutive pop-ups with different email addresses.

What other things are tied to an Apple ID that might cause those prompts to fire? If it helps, I've noticed they seem to be triggered mostly when cellular service is bad (losing service and reconnecting) or possibly shifting to a different cell tower. I rarely if ever notice on wifi.

One note -- I also checked all my purchased music to make sure it was my Apple ID being used. However, I don't know if there are other music files that are not in my "Purchased" folder that might have a different Apple ID linked, but that info seems buried enough that I wouldn't even know where to begin searching. It would be a needle in a haystack given my 10s of thousands of songs.