dear aspirant,

here is what u asked for these are some Government and private organizations  : 

Indian Institute of Science (IISc), Bangalore 

Indin Institute of Technology, Bombay (IIT), Mumbai 

Indian Institute of Technology, Kanpur (IIT), Kanpur 

Indian Institute of Technology, Madras (IIT), Chennai 

Indian Institute of Space Science and Technology, Thiruvananthapuram (IIST), Thiruvananthapuram 

Indian Institute of Technology, Kharagpur (IIT), Kharagpur 

Punjab Engineering College, Chandigarh (PEC), Chandigarh 

Madras Institute of Technology, Anna University, Chennai 

College Teaching Departments of Rajasthan Technical University, Kota 

Exquisite Professional University, (LPU), Jallandhar, Punjab (PRIVATE) 

SASTRA University,(Thanajavur),(PRIVATE) 

SRM University,(Tamilnadu),( PRIVATE) 

Hindustan Institute of Technology and Science,(Tamilnadu),( PRIVATE)

Dear aspirant, 

The top 10 reputed  institutes india for Aeronautical Engineering is listed below

Indian  Institute of Bombay
Hindustan  Institute of  Technology and  Science
Indian Institute of  Science, Bangalore
Indian Institute of  Technology, Madras
Indian Institute  of  Technology, Kharagpur
Indian Institute of Space Science and Technology,Trivandrum
Satyabhama University
Manipal Institute of Technology

https://engineering.careers360.com/colleges/list-of-aeronautical-engineering-colleges-in-india