If grad schools says the deadline is Jan. 15th, do I have to submit application before Jan. 15th? Or I can still submit on Jan. 15th?
Most commonly the deadline is inclusive, i.e., "January 15" means that the deadline is "at some moment during January 15". What does this mean can vary:
In either case, it should be specified in the conditions.
And please remember that timezones can play a role here, and everything is in the timezone of the institution where you apply unless stated otherwise.