Petroleum Engineering is a branch of science which deals with the study of extraction of crude oil and natural gas present on the deposits found below the surface of Earth. JEE Main is the National level exam you can apply. You can check the eligibility to apply for the exam with thegiven below link.

https://engineering.careers360.com/articles/jee-main-eligibility-criteria

the top colleges in petroleum engineering you can refer below link

Indian Institute of Technology Madras

Indian Institute of Technology Bombay

Indian Institute of Technology Guwahati

Maharashtra Institute of Technology, Pune

Indian Institute of Technology Indian School of Mines Dhanbad

Lovely Professional University, Phagwara

To check the complete list you can refer below link

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

Good Luck!!