Nope! ONGC don't offers any of such courses after 12. So you have to go for BTech course in any other college. After your BTech you can qualify the GATE examination and you can opt for PSU's like ONGC, BHEL etc.

To know more about PSU through GATE visit the link below:

https://engineering.careers360.com/articles/psu-recruitment-through-gate-2021

There are many institutes for BTech in India both private and Government. Some of the colleges are:

IIT Bombay - Indian Institute of Technology

COEP Pune - College of Engineering

IIST Thiruvananthapuram - Indian Institute of Space Science and Technology

IIT Madras - Indian Institute of Technology

DTU Delhi - Delhi Technological University

For more colleges visit the link provided below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india

I hope this answer helps. All the very best for your future endeavors!