JEE
Birla Institute of Technology & Sciences - BITSAT
COMEDK Under-Graduate Entrance Test
Common Entrance Test Karnataka
Engineering Agriculture and Medicine Common Entrance Test
EPSI National Admission Test (ENAT) - Manipal University
Rajasthan Pre Engineering Test
Rajiv Gandhi Institute of Petroleum Technology Entrance Exam
Uttar Pradesh Technical University State Entrance Exam

No,u can get petroleum engineering through jee mains marks but not all colleges have this course.Search for college which give btech in petroleum branch, like pdpu offers this course

There are many entrance exams for engineering in india. There is no separate entrance exam for petroleum. The entrance exams are common for all the engineering branches. You have to take the exam and if you passed in it. Then depending upon the marks and relative rank you can choose your interested branch.
Some of the entrance exams are jee mains and there are state wide entrance exams for engineering in every state. Along with that there are many  good private universities from where you can also take the petroleum engineering.

All the best....