It sounds like through a typo or cluelessness or what have you that someone else signed up for that Apple ID before you, so it "belongs" to them now.
There would be some things they could not do with it unless they verify a different email address as primary though since obviously they don't have access to your real email account.
But anyone can create any possible Apple ID by making up any possible ID in an email address format, whether or not it is a real email address of theirs, what matters are the verified email addresses within it at appleid.apple.com.
You would need to pick another Apple ID though. It would be a security breach at this point to someone else if you managed to take that Apple ID from the other person regardless of their mistake.