Hello Mukunth,

To join Merchant Navy after doing B.Tech in Mechanical Engineering there is only one way by doing Graduate Marine Engineer (GME) course from the college such as Anglo Eastern, Great Eastern etc. Who have their own colleges. So that it will be better for you as you don't have to search for shipping companies after doing the course.
It is of around one year of course in which you also have to do on-board training on ship to complete your course.
Do remember that you have to go through a Medical test which will be conducted by the Doctors approved by D.G. Shipping. Also, if  your eyesight is above 6/12 or 2.5 than you won't be able to clear your Medicals as it is the minimum requirement of D.G. shipping regarding eyesight.

I am providing you the link of companies where you can check all the relevant details for the admission and course
http://www.angloeasterncollege.com/?page_id=380#2

Hope this will help you. Feel free to ask any query.

Hello Mukunth,
After complete B.tech, you have to appear in exam GME.
You can join Merchant Navy in the Engine department after doing BE Mechanical Engineering. For this you have to do a GME( Graduate Marine Engineer) course for an year and then get placed in the shipping company as a Trainee Marine Engineer.
Read this article, link given below
https://engineering.careers360.com/news/marine-engineering-training-meti
Thank You.