I have seen native speakers use both variations.
See you Monday.
See you on Monday.
I would like to know which usage is correct or if there are any specific instances in which each is used.
The first is a little more casual than the second, and possibly found more in American English than in British English.
"See you Monday" is more colloquial. For instance, you would say to a friend "See you Monday!", but if you were making an appointment for something more formal it would be correct to say "See you on Monday". The word "on" is implied in the less formal statement.