Do I have a virus or a malware on my iPhone?

You don't have a virus or malware. These messages are designed to get you to purchase unneeded software. Clear your cache and ignore them.

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

DaleBevins Said:

"Do I have a virus or a malware on my iPhone?: Keep getting these two message while surfing internet on my iPhone. Do I have a virus or malware ."

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Thank you for the screenshot.

It is a Scam:

What you are reporting is a scam. So, report it to Apple (and to your federal government, if desired) modify your credentials. Use my User Tip: Using the Photos App to Report Scams - User Tips

Did you Interact with it?

If you did not interact with the messages, then you can ignore it. If you did (i.e. Provide personal info), then you may need to take thinks a step further.

Modifying your Credentials:

Having so much suspicion, consider modifying your credentials, ASAP, starting with a new password.

• Modify: your login credentials (using both a New eMail and a New Password) for Apple and each and all sites
• Associate: a different method of payment to your account
• Enable: Two-Factor Authentication for Apple ID PayPal and for all other accounts that have such an applicable option

It’s an ad designed to scare you into buying useless software.

Close it out, clear the safari cache.

If you don’t want to see such things, install an ad blocker.