I keep getting emails that my storage is full. Is this legitimate or not?

Hello PatriciaStrachota,

Without seeing the email, knowing the email sender, and having the email headers it's impossible to tell whether or not you're be scammed, phished. My advice is to never click on links or attachments from unknown senders. You can do everything from your iPhone without having to click on any links or buttons within emails. I'd ignore this and check your storage within the Settings app.

1. Open Settings
2. Tap on General
3. Tap on iPhone Storage

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

I hope this helps!

Who sent you those e-mail messages? Apple never sends such e-mail messages.

Looks like it's not legit.

See -> Recognize and avoid phishing messages, phony support calls, and other scams

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

See also -> If you think your Apple ID has been compromised

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