I have a new apple ID but my old ID keeps popping up. how do I delete the old ID

Where is it appearing, on an iOS device, computer's iTunes ? Anything that you downloaded on your old account will remain tied to that account, all downloaded are permanently tied to the account that downloaded it (so only that account can potentially redownload those purchases, download updates to its apps, and do in-app purchases in them). If this is on an iOS device then are you still logged into that account anywhere on it (Settings > iTunes & App Store ; Settings > iCloud ; Settings > Messages ; Settings > FaceTime) - you can go out of an account, but only iTunes Support can potentially delete an account (which would also delete its purchases)