How do I stop Safari virus pop-ups on my iPhone?

The website(s) are apparently compromised, either accidentally or deliberately, by scammers. This is very common on sites that purport to give you something for free that normally you'd expect to have to pay for. Follow the instructions MrHoffman directed you to. If that doesn't help, try clearing your web browser's cache and other data (for Safari: Settings -> Apps -> Safari -> Clear History and Website Data).

If none of that helps, then just don't visit those sites.

Regards.

If these are appearing as Notifications in the top right corner, please see the very informative user tip below. 

Stop unwanted Notifications - Apple Community

Tatiana420 wrote:

Did everything but pops keep popping up?

Until proven otherwise, reading the word “virus” means you’re probably reading an advertisement, or reading fiction.

In Settings, disable Popups, and enable the Fraudulent Websites warning, and clear out the saved contents and cache.

Settings > Apps > Safari > Block Pop-ups [on]

Settings > Apps > Safari > Fraudulent Website Warning [on]

Settings > Apps > Safari > Advanced > Website Data > Remove All Website Data

Here is how to: Block pop-up ads and windows in Safari - Apple Support

Tatiana420 wrote:

Still pops up other websites that I haven’t went into trying to stream free movies

Websites often use ad network providers, which means that ads and junk and scams can arrive from most any ad-supported website.

Which is most of them.

Ad networks can either directly allow junk ads, or the ad network providers get breached and then filled with junk ads.

So to confirm, you followed the suggestions I mentioned above, checking the two settings, and clearing cache?

MrHoffman wrote:

Until proven otherwise, reading the word “virus” means you’re probably reading an advertisement, or reading fiction.

For most of these messages that appear out of the blue, claiming that your phone or computer is infected by viruses, "advertisement" and '"fiction" are much too kind as descriptions.

The messages are outright scams, sent by criminals.

The chances of encountering such messages probably goes up quite a bit if one visits dodgy Web sites which claim to offer free access to commercial stuff that normally costs money.

Sketchy websites often present these kinds of ads.

Your only option to never see that kind of malicious ad is install an ad blocker.