HELLO
If you have done your BE/Btech first year from any college excluding IIT's and you want to take admission in IIT from second year onward then it is not possible , you can take admission from second year in the college of same university by lateral entry if you score at least 75% in your first year , and for having admission in IIT's you will have to secure a rank in JEE advance and then also you can take admission in first year not from second year.
And still you have an another option to do masters from IIT's.
Best of luck.

Hey there

If you'll complete your btech first year from non iit college then there is no such exam which will let you enter in iit in 2nd year directly. Though if you are left with an attempt then you can sit for jee advanced to get into IIT but in 1st year like fresher.

Check eligibility for jee advanced

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/articles/jee-advanced-eligibility-criteria/amp&ved=2ahUKEwjDifP236XlAhVi73MBHVCGAdgQFjAAegQIAxAE&usg=AOvVaw01aKmN36HHlgNxEQPk11Z4&ampcf=1

Good luck