Hello, I am getting notifications that my MacBook Air is compromised and being attacked

Sounds like you are getting "phishing" notifications from criminals – probably Web site notifications using custom icons, where the criminals have pasted in a copy of the real System Settings icon, the better to panic and fool you.

Don't click on them or do anything they tell you to do. (Like calling a "technical support" number for "help" – the only "help" you will get is from criminals looking to scam you in one way or another.)

stedman1 wrote:

Please see the user tip below.

Stop unwanted Notifications - Apple Community

That user tip is good as far as it goes, but I'd make one addition:

"Clicking them will cause another website to load, which will subsequently attempt to deceive or frighten you into downloading and installing something you do not need."

Such Web sites might also try to get you to contact "tech support", "customer service", the "billing department", "Apple", etc. to resolve the supposed issue. If you do, you will subjected to very high pressure, in real time, by a bunch of criminals whose goal is to confuse, panic, and SCAM you.

Please see the user tip below.

Stop unwanted Notifications - Apple Community

If security is a concern…

Update to OS X 10.11, while you’re at it. Any Mac running OS X 10.10 can get to (at least) OS X 10.11.

Or update to more recent macOS, if your MacBook Air supports that.

MacBook Air (Late 2010 or newer) can get to macOS 10.13, for instance.

How to download and install macOS - Apple Support