How can I remove Apple ID that is not mine on my iPhone

Each Apple device is linked/associated with an Apple ID of the person who did the setup.

Activation Lock prevents anyone who is not the owner from using this iPhone.

To unlock the Phone, you need the Apple ID and password of the previous owner, that were used during set up.

So you have to contact the previous owner.

The previous owner has to read -> this Apple article: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch -> What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Then the previous owner has to remove the iPhone from his account, see this Apple article:

Check your Apple ID device list to see where you're signed in

Check your Apple ID device list to find where you're signed in - Apple Support

Then you can sign in with your own Apple ID.

See the following Apple articles:

Activation Lock for iPhone, iPad, and iPod touch

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

How to remove Activation Lock -> How to remove Activation Lock – Apple Support (UK)

• If you need help removing Activation Lock and have proof of purchase documentation, you can start an Activation Lock support request.

Read this before you use a 2nd hand iPhone.

You can also contact Apple support for help, -> Get Support (apple.com)

You have to show proof of ownership of your product, provide all documentation showing your purchase of the device.

If you do not have additional proof of ownership, contact the reseller. They may be able to provide the original purchase document.

Once Apple receive your proof of ownership, Apple will further review your request and provide an update.

See also -> Keep your receipt after you buy an Apple device

Keep your receipt after you buy an Apple device – Apple Support (UK)

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Perhaps you have got a stolen iPhone.

If you can't get in touch with the previous owner, you can't use the iPhone, recycle the iPhone.

I have a 1st generation iPad that my mother purchased and used. She has since deceased and the device is now in my possession. I do have her death certificate but nothing else that shows proof of ownership. I remembered the password to unlock it and use it which I have done and now I have personal information on the device. But I do not know her apple id and password so therefore I cannot make purchases in the app store or do anything else that requires an apple id and password. So, does the statement "If you can't get in touch with the previous owner, you can't use the iPhone, recycle the iPhone" still apply? Surely there is a solution to this. Please help.

Ovation, in your case of it being a family member please see How to request access to a deceased family member's Apple account - Apple Support