Make an account with China Southern Airlines (if you haven't already). Add your booking to your account (if that's not there already). The page should look like this https://oversea.csair.com/tka/us/en/my/order/ .
Then you should be able to manage your booking directly on their website. That typically includes ordering or selecting meals, selecting seats, change dates (which can be expensive), add luggage, etc.
I want to know how to verify it just to calm myself from worrying if I booked in the legit website.
You only need to worry if you put your name and your booking code into Southern China's website and they come back with a message "booking not found".
Btw I booked from skyscanner’s link directly to china southern airlines
You are fine then. Skyscanner is a very reputable website and booking directly on the airline's website is the best way of doing that.
Update from the comment
The booking reference I got starts with “Go” and ends with 707.
The booking reference or PNR (Passenger Name Record) is a six digit code made from letters and/or numbers.
Could it be possible that it’s too early to check it since only been few hours and may not be reflected yet?
Not really. The booking reference gets issues right away, so you should be able to see it in your account. It can take up to 24 hours for the ticket to be issued (which is an paper work thing), so there is no harm in trying again tomorrow.
Email came from czmp@csair.com is this the legit one?
Yes. That's legit. Your booking is fine.