Check the App Store and iTunes Store to see if there are any updates for apps/purchases. A request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. After deleting the apps, it may be necessary to restart the device/computer before you can download the apps again. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID.
Purchase History Review. *
If you forgot the Apple ID (iCloud) password, enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option. Link to contact Apple Support at the end of the 2nd article.
Apple ID - Manage -
Apple ID – Forgot Password *