Yes you can get admission through sports quota in many top B.Tech colleges in India, but it depends on which type  of sports achievements you have. To get eligible for this generally you have to represent your state or country on national or international level.You should have proper certificates also.

Getting admission in IITs or NiTs is not possible because they do not provide sports quota.So you can check many state level and other colleges according to your preference.

Yes, you will get admission through sports quota in some top colleges in India for B.tech. admission process is based on both academic and sports achievement.there are very limited seats for sports quota,There is best engineering colleges allot 5% of the total available seats. You need to provide certificates of participation in sports state , national or international level while applying addmission and also you may need to attend trials or fitness tests during admission process.