Yup, these sound like illegitimate messages. You should definitely scan your computer for malicious software. You can try these free programs to scan for malware, which work with your existing antivirus software:

• Microsoft Safety Scanner
• MalwareBytes' Anti-Malware
• Anti-Rootkit Utility - TDSSKiller (for more info, see this alternate TDSSKiller download page)
• AdwCleaner (for more info, see this alternate AdwCleaner download page)
• Hitman Pro
• ESET Online Scanner

Further information can be found in the Troubleshoot Firefox issues caused by malware article.

Hope this helps.

I have typed my question in the subject line above. I am getting VERY annoying pop-up icons saying Viruses Found Antivirus notification. Also, pop-up icons saying Attention! Click here to secure your data! The websites shown don't look like Firefox sites so I am reluctant to click on them. I have tried closing or dismissing the popups numerous time but they continue to reappear HELP!!

Are these small popups stacked on the bottom right corner of Firefox windows?. If so then these may just be Web Push Notifications from sites you have allowed to send you notifications. Instead of useful information, some may instead send you junk, spam or fake virus/trojan/antivirus alerts to try and get you infected. You can revoke these sites from sending you notifications.

https://support.mozilla.org/en-US/kb/push-notifications-firefox https://support.mozilla.org/en-US/kb/push-notifications-firefox#w_how-do-i-revoke-web-push-permissions-for-a-specific-site