IIST takes admission through JEE Advanced. 

Candidates should appear for the Joint Entrance Examination Main conducted by Central Board of Secondary Education (CBSE), New Delhi to qualify themselves to appear for Joint Entrance Examination Advanced conducted by IITs and secure the minimum prescribed category-wise marks in JEE (Advanced)-2017 as given below : a. General Candidates (GEN): At least 20% marks(i.e.73 marks out of 366) in aggregate and at least 5% marks (i.e. 6 marks out of 122) in each of the three subjects (Physics, Chemistry and Mathematics).

b. Other Backward Community – Non Creamy Layer OBC (NCL) Candidates: At least 18% marks(i.e. 65 marks out of 366) in aggregate and at least 4.5% marks (i.e. 5 marks out of 122) in each of the three subjects (Physics, Chemistry and Mathematics).

c. SC, ST & PD Candidates: At least 10% marks(i.e.36 marks out of 366) in aggregate and at least 2.5% marks(i.e. 3 marks out

No, there is no such entrance test as you will have to clear Jee Advanced exam if you wish to get admission there. Fore reference, you can go through the below article -

IIST 2017 admission criteria

Good Luck!!!