Hey Sulakshna !

Yes, of course you can choose IIT Patna as your reporting centre for the verification of documents. The system generally wants the document to be verified at one of the IITs nearest to you, it has no relation in terms of where you gave your Advance Exam.

But it's generally favourable to be in home state for transportation issues, either way, it won't matter.

Hope this helps

Good Luck !