There is definitely a priority of exams for engineering you can choose to give as per your interest.

The exams are:

• JEE MAINS
• JEE Advanced
• BITSAT
• VITEEE
• SRM JEE
• MHT CET
• Amrita

I have hyperlinked the exams for you. In case you want to know more about them in detail then you can click and check the details.

Hope this helps you.

Good Luck.