It sounds like you may have been scammed if I am understanding your post. You should never enter an Apple ID into your phone that is not yours. People will try and talk you into this for a number of reasons. Once you enter the Apple ID, all they need to do is change the password and your device is now locked to their account.
You are now stuck proving the device is actually yours and not the person's who has their Apple ID in there. This will require the original purchase receipt from Apple or Authorized Apple Seller to remove the lock that is now on your device. A third party receipt will not be accepted. With that information, you can start a support request to remove the lock by following the link at the bottom of this Support Article:
How to remove Activation Lock - Apple Support
Activation Lock is a feature on your device that prevents anyone from being able to use your phone if it is stolen. The device is locked to your Apple ID and if they attempt to reset it, then they will see the Activation Lock Screen that tells them that it is Locked to the Owner. The only way to remove the lock is to enter the Apple ID and Password or use the link above with the documentation to remove the lock.