Engineering in Maharashtra

Yes, of course you can. All engineering college get the admission through CBSE or state board. You can easily get the admission anywhere in India.

1st CET results will come then go to nearest college where you will purchase/get brochure and kit for login. Then fill the form as per instructions are given in brochure. Next steps are well explained in the brochure.

With 96 marks in JEE Mains and having OBC category, it's quite difficult to get into any NIT/IIIT.
However you reside in Maharashtra, so there are fair chances that you will get admission in the govt. /private colleges of Maharashtra. So keep visiting your nearby colleges and gather information.

Firstly, OBC is not a caste, it's a category. Quickly coming to your answer part, yes, you can get admission in Maharashtra colleges with your JEE marks.