Both “see you Friday” and “see you on Friday” are correct. It just depends on the level of formality.
“See you Friday” is more casual and colloquial. It’s commonly used in informal conversations between friends or colleagues to say goodbye for the week.
“See you on Friday” is slightly more formal and precise. Using “on” explicitly states that you will see the person on the day of Friday.
So in informal/casual contexts, either one is fine. But “see you on Friday” follows standard grammar rules more strictly if a bit more formality is needed. Both convey the same meaning of seeing someone on the upcoming Friday.