Unauthorized purchased

That is very likely a scam rather than an actual purchase. If the only indication of the charges is from an email or text, be aware that it may be a phishing attempt to get you to log in to a site that appears to be Apple and divulge your password or credit card information. See: Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

and Identify legitimate emails from the App Store or iTunes Store - Apple Support

If it is a real charge, see the following instructions. They include information on contacting Apple Support if the other steps don't help: If you see apple.com/bill, itunes.com/bill, or an unfamiliar charge on your statement - Apple Support

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

If the charge is not there, then what you probably were scammed.

 Did you 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.

If you gave you Apple ID password to a scammer, 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

Learn about Phishing, Scams, 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

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

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

For 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

Identify scams related to purported apple notifications--See what Eric Root says above.

Learn about/Increase security

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

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.