if I want to do MS in aeronautics in a foreign country (where there is scope to grow) , in which branch should I pick in my B.tech (preferably in an IIT College) and what exams should I clear before I graduate to serve all the criteria to be eligible to do my MS in aeronautics in a foreign country.

If you are thinking of doing MS in Aeronautics then i would suggest you to go for Aerospace Engineering or Aeronautical Engineering in your Btech.

You can also do Mechanical or Civil as it is also considered but as you have specially Mentioned, which one then i would suggest the above, Aerospace or Aeronautical.

For doing MS there are various exams depending upon the requirement of the particular University. Some requires TOEFL score while some GRE. So, you need to find out the proper University for you. There are certain other requirements like SOP, LOR and good grades in your UG.