How can I stop virus pop-ups on my Mac mini?

Somewhere along the path, you were offered notifications by a website or other such, and accepted them.

Now you no longer wish to receive those notifications.

Here is how to remove the permission to send notifications, and how to prevent future offers of notifications:

Stop unwanted Notifications - Apple Community

There is no malware here, no “virus”, no “hack”, just spam.

If this is the usual offer, probably an advertisement for a product you don’t need, and that badly solves a problem that hasn’t existed for a decade or so, and that doesn’t even address what the pop-up advertisements were claiming. But the likely product being offered (a VPN) badly solves the problems you don’t have in a way perfect for collecting personally-identified metadata.

That is a "phishing" scam message.

The phrases "Apple security system", "Hack detected", and "check security" are bald-faced lies.

Never call any phone number that you see in such messages. These phone numbers may belong to criminals who pose as "tech support" – the better to rip you off, or to fool you into installing remote access software, etc. on your computer.

As for any software that the messages are pushing, if scammers want me to install that software on my computer, that seems to me to be a good reason not to install it!