With 91.76 percentile and an OBC-NCL rank of ~39,000, getting top NITs or IIITs is difficult, but you might still get lower branches in newer NITs or IIITs in later rounds.

Possible Options (in JoSAA Round 5-6 or CSAB Special Round):

NITs (Low-Demand Branches, Home State Advantage helps):

NIT Sikkim

NIT Meghalaya

NIT Mizoram

NIT Nagaland

NIT Arunachal Pradesh

IIITs (Less Competitive Ones):

IIIT Bhagalpur

IIIT Una

IIIT Kalyani

IIIT Manipur

IIIT agartala