I am expecting 15000 rank in JEE Mains. Which colleges should I prefer during counselling?

With this rank you can get nits like the one in patna, durgapur(a slight chance).But I would suggest you,that you give equal preference to IIIT’s. In the past few years they are getting better than certain NITs. Among the iiits for your rank IIIT kancheepuram apparently iiit kancheepuram would be the best choice.