MAT

Score above 600 is considered a good score. You can try for good colleges but at the same time you should also give Feb-MAT.
Some of the colleges with your score are:
Universal Business School, Sion, Mumbai
Lovely Professional University, Jalandhar
Lovely Professional University
SSN School of Management (SSN SOM)
University of Petroleum and Energy Studies
GITAM Institute of Management, Hyderabad
Jagran Institute of Communication and Management, Bhopal

Candidates seeking admission to our Post Graduate Programmes will have to qualify either in CAT / XAT / CMAT / GMAT / MAT

Aman, you will not be able to get good colleges with your CAT percentile. With MAT percentile you can apply in:
Amrita School of Business - Department of Management Studies
Acharya Bangalore B-School (ABBS)
Indus Business Academy (IBA Bangalore),
Institute of International Trade
https://www.shiksha.com/mba/colleges/mba-colleges-in-india-accepting-mat-score?

Good Morning Varun,Yes you are eligible to give GD/PI round for ICBM-SBE.This college give least preference to your score but it gives more weightage to how you present yourself in the GD/PI rounds.

I don't think that this score will take you any close to a good institution. you have the option of taking it again but i don't know if you will make a marked improvement on this score. Generally Aptitude tests are the test of what has been learnt over the last number of years as they reflect your aptitude for higher studies. But you should try it anyways and see how it goes.
All the best !

Mat scores not considered for admissions in Tapmi

Mat scores not considered for admissions in Tapmi

Tapmi does not consider mat scores for admission

In 2015 the cutoff for PGDM main course was 75 percentile for CAT and 80 percentile for MAT. As you have a fairly high score in MAT there is a high probability that you can get admission in PGDM main course. As regarding specialization , First year of PGDM is common for all students and option to choose desired specialization would be given in second year, so you can choose specialization of your choice.