Does IIIT Delhi have its own M.Tech test?

Yes, IIIT Delhi does have its own M.Tech test. Here are some details on its entrance test for M.Tech CSE- 

As for the eligibility, you must have scored at least 65% aggregate (CGPA*10) in your qualifying degree. If eligible, you’ll face a written test in which you’ll be grilled on CodeChef. Upon qualifying that, you’ll face a panel of three professors. On successfully qualifying for the interview, you’ll get admission into IIITD as an M.Tech CSE student. 

These are all the details on M.Tech CSE admissions at IIIT Delhi.