I am receiving from < swicalicistable.com> this message"Security Alert You've visited illegal infected website".Then they want me to use their scan.

Yes, the message is definitely a scam. No, you should not use their software. If you could tell us how you are receiving these messages, we could provide further steps.

Are they website popup messages?

Emails?

Notifications?

Phony "tech support" / "ransomware" popup… - Apple Community

The way to resolve them is to follow the instructions in Stop unwanted Notifications - Apple Community.

For notifications, please see the very informative user tip below. 

Stop unwanted Notifications - Apple Community

For notifications, please see the very informative user tip below. 

Stop unwanted Notifications - Apple Community

Like stedman1, I am receiving popups sliding in from the upper right of my screen saying "Security Alert You've visited illegal infected website...with illegal content. Your Mac is at risk of being infected by viruses. To continue browsing safely - perform an antivirus scan.

This is from swicalicistable.com.

I am getting variously worded pop ups from the upper right of the screen.

What do you suggest? Thank you.

The messages are pop ups on the corner of my screen. It highlights the need to perform a scan through various programs. In some messages it names Norton, in others, McAfee, mac uptodate, mac scan required, McAfee total security highlightening that I have a Trojan virus.

Hi, I was intereeested to know how to resolve the situation described in Atab-btab above. It is the same problem Morgan Rauch described. It seems he had a satisfactory answer. I stilll have the virus warnings popups coming in from the upper right of my MacBook Pro desktop.

Thank you.

You are quite welcome, and thank you for the feedback.