How do I get a refund for an unauthorized purchase

See your purchase history for the App Store or iTunes Store https://support.apple.com/en-us/HT204088 to see if the charge was made by Apple. If you think you are owed a refund, see Request a refund for apps or content that you bought from Apple  https://support.apple.com/en-us/HT204084

and How long refunds from the App Store or other Apple services take https://support.apple.com/en-us/HT210904

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But, I am concerned that you may have been scammed. Apple does not make many billing errors.

Did you possibly provide any potentially damaging information to anyone? If yes, you'll need to follow up, for example, with a credit card company, Apple, Social Security, your bank, etc.

Could you have given Apple ID password to a scammer If yes, then:

Change your Apple ID password https://support.apple.com/en-us/HT201355

Here is What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

To be proactive, learn about phishing, scams, and Apple practices, etc., see:

If you see apple.com/bill, itunes.com/bill, or an unfamiliar charge on your statement https://support.apple.com/en-us/HT201382

Identify legitimate emails from the App Store or iTunes Store https://support.apple.com/en-us/HT201679

How to avoid scams when using Apple Pay to send and receive money https://support.apple.com/en-us/HT208226

This scam related information from Apple including reporting scams to Apple see Avoid phishing

emails, fake 'virus' alerts, phony support calls, and other scams https://support.apple.com/en-us/HT204759

How to identify scams related to purported apple notifications—per Eric Root.

“Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address. The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple emails won't have poor grammar/misspellings. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers. …The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.”

While scams and activities that compromise an account are different, learn about/Increase your security for safety. See:

If you think your Apple ID has been compromised https://support.apple.com/en-us/HT204145

Increase the Security of your Apple ID https://support.apple.com/en-us/HT201303

iCloud security overview  https://support.apple.com/en-us/HT202303

Ways to keep your information safe on Mac https://support.apple.com/en-gb/guide/mac-help/mh11402/mac

Use Two-factor authentication for Apple ID https://support.apple.com/en-us/HT204915