Do I need to appear in any exam for pursuing Statistical Data Science in ISI?

The cutoff marks for taking admission in ISI college are divided on the basis of your category 

The All students must be passed in 12th and 10th with 50 percent marks

For General Category  if you are a general category students then you must be score above 90 to 95 percentile for a top branch 

No, just because you apply in the B.Stat entrance test and get a crack does not like directly merit you with an admission into the ISI Delhi BSDS program.B.Stat and BSDS are different programs at ISI and have both a different admission procedure and requirements. Admission in the B.Stat programme is mainly done by the own strenuous entry exam and interview of the ISI. On the contrary, the process of BSDS admission is not related to the ISI particular entrance exam and depends on your grade in JEE Main or CUET (UG) (Mathematics and English).This is why you need to have a separate application to BSDS and fulfill its requirements.

Yes, if you are in your 4th year of a CSE program, you are eligible to apply for the M.Stat programme at ISI, provided you have a strong background in mathematics and statistics, as you can apply with a BE/BTech degree with statistics as a subject; however, it's important to check the specific eligibility criteria on the ISI website for the latest information.