Why does iPhone keep asking for iCloud apple ID password?

I don't use iCloud and I never have, but the other day my friend added me to a reminders list using iCloud and I added myself but I don't use iCloud so I just signed in with my Apple ID and it worked, don't ask me why. I've turned off iCloud now, but still, every few minutes a bubble will pop up saying to give my Apple ID password for iCloud so I type it in but it says its incorrect.
I tried to reset my password but I don't use the email that I signed up with anymore so I can't email myself a link.
I'm on iOS 9 with an iPhone 4S btw. I don't know if that will help but:/
also, this is a really big problem because I can't even download off the App Store anymore since it says my password is wrong.

ICloud is a cloud storage and cloud computing service, if you want to get it you need to input its id and thats why apple is asking again and again and do Install Leo Privacy Guard, it provides you data monitoring system, through which you could keep record the usage of your each data usages. It is also helpful in securing your device totally by its various astounding features.

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