If it only pops up when updating or purchasing then there are apps or purchases still affiliated with the account. I would delete any apps that are tied to the old Apple ID and redownload with the new Apple ID. if you can't tell which ones they are I would try updating apps one at a time and see which apps prompt for the old Apple ID, delete those and redownload. As far as it asking for the old Apple ID with New downloads, I would double check in Settings>Your Name>iTunes and App Store that it shows your current Apple ID.
So I had an old iCloud account. Like used in 2012. Maybe earlier. But I stopped using it due to the fact I thought someone else had access to it. So I made a new one. It’s been a long time since I’ve used it. But now it came back up. I’m using my new account for App Store and updates and iTunes. But it won’t let me update or download new stuff. Unless I give the password to the old account. Which I don’t know. Then it wants me to go into account recovery. And I no longer use the number that’s associated with it. What do I do?
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User profile for user: DanielShartzer
Question: Deleting an iCloud account.