Hello Shree,

No you can't get into ESIC medical college but yes, there are other top private college in India which charge capitation amount based on your marks and rank in NEET exam.

If you are not going through management quota then refer this information:

Employees State Insurance Corporation(ESIC) Medical College ESI Joka (ESI MC Joka Kolkata) is one of the premier govt medical colleges. The medical college Founded in the year 2013 under the aegis of the ESI Corporation, a centrally controlled autonomous body.
ESI MC Joka Kolkata, Famous to provide high-quality education and modern health-care. The medical college and the medical courses are recognized by Medical Council of India. The Employees State Insurance Corporation Medical College is expecting to get the permission from Medical Council of India to take admission of eligible MBBS students for PG medical courses from the year 2019.
Eligiblity Criteria :

10+2 with Physics, Chemistry, Biology & English individually with a minimum of 50% marks (40% marks in case of SC/ST & 45% marks OBC Category) taken together in Physics, Chemistry & Biology.
INTAKE : 100 seats
FEES STRUCTURE :
AIQ Fees (full course) - 100,000
Amount to be paid in time of admission - 55,000
HOSTEL Fees (Boys & girls in campus) :

4,200/month(Internet, Laundry, Ac, Power Backup available)
NEET CUTOFFS :

GENERAL : 6800
SC : 46383
OBC : 7636
.
For more information about this college please refer this link:
Here is the link:
https://www.careers360.com/colleges/esic-medical-college-hyderabad

Hope this helps.

Thank you and all the best.