Which course should I do which can be done parallel with B.Tech (branch - IT)?

You can do C, C+ and Java courses in some nearby computer centers or through online courses. That will help you during your placements.

You can go with summer training and winter training programme in the end of your 1 year or other. Basically, on the continuation of the course you can attend the workshop which relate to IT. Take training in networking, Big Data, etc. There is no course which you can pursue in parallel.