How can I delete an Apple ID that's not mine

You likely have content on your phone that was put there by somebody else who used the phone, either when you lent the phone to somebody else, or by a previous owner. If you lent the phone to somebody else, ask that person what they downloaded, then delete it. It may be an app trying to update with their Apple ID. If you bought the phone used, the seller did not do as instructed in this Apple article:

What to do before selling or giving away your iPhone, iPad, or iPod touch [or if you received one that had not been erased] - "Use these steps to remove your personal information from a device, even if you don't have it anymore." Click here --> https://support.apple.com/HT201351