See you can obviously apply for GATE with your qualifications in the final year of your BTech. Although most of the IIT's/NIT's will not accept application for MTech Aerospace from your field of study. So there can be some private colleges which can allow you to pursue for MTech which you have to inspect by visiting the targetted universities. In general Mechanical Engineering, Aeronautical Engineering, Aersopace Engineering are held eligible for this course for most of the case.

Some of the best colleges for Aerospace Engineering are:

Indian Institute of Technology Bombay
Indian Institute of Technology Madras
Indian Institute of Technology Kharagpur
Indian Institute of Technology Kanpur
RV College of Engineering, Bangalore
Indian Institute of Engineering Science and Technology Shibpur
Punjab Engineering College, Chandigarh
Manipal Institute of Technology, Manipal
SRM Institute of Science and Technology, Chennai

I hope this helps.