iPhone keeps asking to sign-in to old Apple ID?

You will either need to get the old account working again or you will have to hope you kept your receipt from Apple when you purchased the iPhone from them.

Apple has two related features, Activation Lock ( Activation Lock for iPhone and iPad - Apple Support ) and Find My ( iCloud+ - Find My - Apple ), which are designed to prevent anyone else from using an iPhone, iPad, or iPod touch if it's ever lost or stolen. Deactivation ( How to remove Activation Lock - Apple Support ) of either requires knowing the Apple ID and password that set the feature, or by placing a special request to Apple to reset the device. This Apple ID information essentially defines the current ownership of the device. If you do not know the required information, or do not have an Apple accepted proof of purchase, the device is otherwise useless to you.

Here are additional resources to recover account information or there is an Apple accepted proof or purchase

• For help with a forgotten Apple ID password, click here --> If you forgot your Apple Account password - Apple Support Also look into using Account Recovery This support article has various country telephone numbers for contacting Apple for extra support and service in doing that since you do not have access to the old email account. ➔ Contact Apple for support and service - Apple Support

Failing that, Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. This is done online* at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not provide many details in the article as to what is acceptable proof. Prior to this official service Apple typically required the original receipt** issued by Apple or an Apple Authorized Reseller. Note that while this will let you get use of the device again, it will not help you with lost access to an account.

* There is a special link for this service. To save time you should use it instead of https://getsupport.apple.com/

**Apple recommends you keep your receipt after you buy an Apple device. --> Keep your receipt after you buy an Apple device - Apple Support

Apple ID and Activation Lock

iCloud uses Apple ID credentials.

If you do not remember the Apple ID Password then follow the steps given in this Apple Article -> If you forgot your Apple ID password - Apple Support

If you do not remember the Apple ID then follow the steps given in this Apple Article -> If you forgot your Apple ID - Apple Support

If you are the owner or the owner has shared all information with you then to open Activation Lock:- If it is Activation locked, read here --> Turn off Activation Lock - Apple Support Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Learn how to remove a device from a previous owner's account.

If you are not the owner and do not have the Apple ID and Password then there is no way that you can get into this iPhone unless the original owner shares the Apple ID and password with you. If you are lucky you can get into this iPhone if they (owner) accidentally remove the device from their Apple ID.