Hey there

Yes there are Colleges which provides Mtech in construction technology and management like

Cochin University of science and technology Kochi. 

Check the list of colleges in Kerala

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/list-of-me-mtech-in-construction-technology-and-management-colleges-in-kerala&ved=2ahUKEwifvcePlbHjAhVEq48KHZCWCDEQFjAEegQIBhAC&usg=AOvVaw3FxUVzEoDn5YbQzoXVgGPc&cshid=1562995961640

Good luck

Hello!
The above course is provided at IIT Madras and IIT Bombay.
Following are the colleges providing mtech in Construction Technology And Management Colleges
1. Bennett university, greater Noida
2. Lovely professional university, phagwara
3. Mit world Peace Pune
4. Cochin university of science and technology, Kochi
5. MES College of Engineering, Malappuram

Here are the four colleges offering MTech in Building Technology and Construction Management in Kerala-

Indira Gandhi Institute of Engineering and Technology for Women

MES College of Engineering

Sri Narayana Gurukulam College of Engineering

ToC H Institute of Science and technology.