The situation you describe often happens if there are apps (or media purchases) on the device that were installed (or downloaded) under a different Apple ID/account, and they need updating or redownloading. This can sometimes happen if a device was not properly reset by a previous owner, or if you incorrectly "change" your ID by creating a brand new Apple account instead of as in: Change your Apple Account primary email address - Apple Support
If you think this is what is happening then the best way to resolve this is to delete the item(s) requesting the update, and then download it again using the Apple ID that is signed in with the device. If you do not know which apps these are, change to manually updating apps on your device (see How to manually update apps from the App Store - Apple Support ). Go through your app list and update them one by one. The problems apps will prompt for a different account.
Also check the account entered in Settings > Media & Purchases and make sure it is yours. If you lent your iPhone to somebody they may have downloaded the app with their account and changed the setting there.