Will I get home state and ESM quota in YMCA, Faridabad to pursue B.Tech with 211478 rank in JEE Mains and 66000 OBC rank (Haryana)?

Candidates wishing to take admission in BTech at Ramaiah Institute of Science and Management have to appear in JEE Main, JEE Advanced, CUET-UG, SAT, KCET, COMEDK. So, yes even if you have not appeared in JEE, you can produce score card of any of the above mentioned exams. 

The East Point Group of Institutions accepts many exams for the BE course. The accepted exams are JEE Main, COMEDK, and KCET. Students can appear in any of these exams to get admission at EPGI. Students need to fulfil the eligibility criteria as well.

Amrut Institute offer admission in BTech and Diploma in Engineering based on merit in last qualifying exam. So, no JEE Main is not compulsory to take admission in Amrut Institute courses. 

With 57.8 percentile in JEE Main and 73% boards, getting CSE/AI in top government colleges is unlikely. But you still have good chances in private colleges through UPTAC/AKTU or direct admission.

Possible options:

KIET Group of Institutions

ABES Engineering College

Galgotias Coll

JEE (Main) cutoff for BTech in Computer Science and Engineering in Sagar Institute of Science Technology and Research, Bhopal in the closing round has ranged between 3,75,232 to 10,07,060 from 2021 to 2023.