As per official notice by DASA, from 2021 onwards, JEE Main’s Rank has been made mandatory for DASA & CIWG Scheme (for taking admissions in NITs/CFTIs).

Because you are in Class 11th in the year 2019-20, you would be applying for DASA in the academic year 2021-22.
Hence, you will have to appear for JEE Main 2021  (January and/or April Exams) for which you would be registering in Sept 2020 (JEE Main January).

You can also appear for JEE 2022 for DASA 2022. In all the years after 2021, JEE Main’s Rank will only be valid for DASA Scheme.

JEE Cutoffs for Admissions under DASA:

Based on the General  JEE Cutoff & the number of seats in a particular NIT/CFTI (15% & 5% seats for Dasa / CIWG), the DASA / CIWG Cutoff will be set for the particular year.

Because DASA is to intake students on the basis of SAT Subject Tests’ Scores (till session 2020-21), it is not fully predictable of what would be the JEE cutoff for DASA.

Note that: JEE Mains Cutoff Rank varies every year (on the basis of percentile of JEE Main’s Scores).  

You can refer to JEE cutoffs (General Category) to get an estimate- JEE 2019 Cutoff in NIT Trichy can be seen here.

To get more of your queries cleared on JEE being mandatory for DASA / CIWG, here is the update. 

For DASA / CIWG Cutoffs of the last few years:-

DASA / CIWG 2018 Cutoff for admission in NITs & CFIs 

CIWG 2019 Round 1 & Round 2: SAT Cutoffs