Which engineering course should I pursue to get good career prospects?

No branch is best or worse. It depends upon one's personal interests. Choose your career by yourself. Personally, I would suggest mechanical, ECE, CSE or Civ for faster growth.

The question can not be answered directly but still, I will like to help you on this. If you do engineering in the branch in which you have interest and will try to make projects, then every course of engineering in its own way will give you a good job opportunity. Hope this answer will help you.