There is no GATE Exam for Petrochemical Engineering. It is a sub branch of chemical engineering. So the syllabus will be of Chemical Engineering which means that you need to attempt Chemical Engineering paper in GATE.

You can check the syllabus for Chemical Engineering by using the link below

https://engineering.careers360.com/articles/gate-syllabus-for-chemical-engineering/amp

You can check the syllabus for Petroleum Engineering by using the link below

https://engineering.careers360.com/articles/how-prepare-for-gate-petroleum-engineering/amp