Can I study m.Ch in cardio thoracic surgery under management qouta (payment seat) in india?

Yes, if qualified. To get enrolled to any post graduate (pg) studies is very difficult, as india has thousands of highly qualified applicants for pg studies. If you are a non indian graduate you have to pass an mci qualification examination, even if you want to pay, your selection depends on your grades, and if you have very good grades, then may have a chance to get selected.