How to remove unauthorized Apple Account associated with my email address?

Is this mail address still listed as your primary Apple Account mail address?

If yes, you should change your Apple Account password as a first step.

Have a look at the related articles, explaining all steps:

Change your Apple Account password - Apple Support

Change your Apple Account primary email address - Apple Support

If you think your Apple Account has been compromised - Apple Support

This is a user to user community, we can not access your personal data. You will have to contact the official Apple Support about this issue, if you can not gain control over your Apple Account this way.

Contact Apple Support - Apple Support

Unfortunately you are not providing much detail and there are a lot of possible scenarios.

How are you finding out about this? There is so much spam and phishing out there these days that my first thought is what you are seeing is one of those. Have a look at Recognize and avoid social engineering schemes including phishing messages, phony support calls, and other scams - Apple Support

Somebody can only create an account using your address if they have full access to your email account to be able to respond to Apple when it sends setup emails to that address. So your concern is really more about who has access to that email account and now securing it. Or did somebody just get as far as you being sent an email by Apple regarding setting up an account? If so, I guess there isn't anything you can do about that. No account was actually set up if they couldn't respond to that email.

Once an account is set up using an address, a second account cannot use that address. That means if somebody else used your address that you presumably have not yourself already set up an account with that address. Even if Apple were to do anything about the account now, you could not set up an account using that address.

You can contact Apple about this. Refer to this page for Apple Support for different countries ➔

Choose your country or region - Official Apple Support

Select your country (if you do not see your country, also look for "other" in regions; e.g., "Other Africa"), then "Choose a product". Click the "show" item under each category for more selections. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

Again, we are just other customers like you. Apple is not here. This is a customer helping other customers website. There is absolutely nothing anybody replying on this forum can do about this. You need to take the action. Since this is a Hotmail address you need to contact Hotmail about regaining control of your email account.

As far as the Apple Account is concerned, what you claim in not really possible unless your email account itself is compromised. You need to take care of that. That would make further use of the account by the other person very difficult, though I can't see that it really makes much difference at this point. If the other person set up the Apple Account then the Apple Account isn't yours even if the email address they used is yours. Even if Apple deleted the account, according to what they say you wouldn't be able to set up an Apple Account with that address for 6 years. -->

From: How to delete your Apple Account - Apple Support

“Can I use the primary email address for my deleted Apple Account to create a new Apple Account or with another existing Apple Account?

No, once your Apple Account is deleted, you can’t use the email address that you used with it to create a new Apple Account for as long as Apple retains the one-way hash of the email address. For third-party (non-Apple) domain accounts, the one-way hash is deleted after six years. For other accounts, this is retained according to Apple's retention policy, which is reviewed regularly. In addition, you can’t use that email address with another existing Apple Account except as a rescue email. Also, if your primary Apple Account email address is with a Custom Email Domain, it can never be reused to create an Apple Account after your Apple Account is deleted, even if the domain ownership changes.”