Kolkata

https://www.google.com/amp/s/www.shiksha.com/engineering/articles/amp/what-after-btech-know-your-options-blogId-14784
This will guide you proper what to do after B.Tech.

Hi, please click on the link given below to know which colleges you can get with your rank:
https://www.shiksha.com/design/resources/nift-college-predictor

There is an entrance exam for this course in Scottish Church Kolkata as I have got to know in 12 years, I think around 150 students were called for the first counselling. So, all the best for the entrance test. You can check out the websites for application.
All the best.

Well, you have a very decent percentile in boards. However, if you are going for colleges like Scottish, Xavier's and many more renowned colleges, there would be very tough competition to fetch a seat. Unless or until you belong to the reserved category, because less no. of general seats are there and having rigid selection process for it.

There is a JELET examination which is held after the admission process through WBJEE exam. You can apply to it. Or, it would be more easier to connect through the desired college, itself because every private engineering college has a management quota to ensure the admission of lateral students through lateral entries.

The following Institutes can meet your requirements.
1. Imagic Learning Solution Private Ltd. Kolkata
2. WLCI School of Fashion, Kolkata.

Hey Vikram,
Yes, you can select this course as you've a good percentage. Here's the link for admission in Techno India. This may help you.
https://www.shiksha.com/university/techno-india-university-kolkata-38061

Hi Tuhina,
It seems difficult as Scottish Church College is very rigid in their admission eligibility rules. Unless you are from a reserved category - then you have a very strong chance of getting through.