I am getting browser telling - its Apple security. "Warning! Your Apple iPhone is severely damaged by 13 Virus!" Is it legitimate/valid message or spam? I just tried to browse one website. Thanks

All such messages are scams from criminals. Close the offending page and avoid sites that are involved in such bogus advertising tactics.

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

Ignore it.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware if it is updated to latest iOS/iPadOS, unless you have intentionally downloaded spurious softwares or unauthorized apps directly from the internet and installed on your device or/and have Jail Broken. 

It (Hacking) also depends on how careful are you in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password etc with your friends and family members.

Be careful when sharing the device's sensitive and valuable information with friends and family members.

Thumb Rules:

1. Enable  Guided Access before handing over an iPhone to kids
2. Don't share Apple IDs
3. Don't Jail Break
4. Don't share sensitive information pertaining to your device and payment methods
5. Beware of Phishing

Ignore. These messages are scams designed to trick you into disclosing your account details, or into buying useless software.