66 percentile in JEE Mains exam is the low percentile for admission in IIT and NITs. But you are free for admission in any of the private college. Every college has its own fundamentals, some take students on the basis of JEE Mains , some on entrance exam, some on 12 percentage, some direct admissions. U can take admissions in any of the private colleges in any of the city or area. U can give any entrance exam for any of the private college or directly talk to college authorities.

hello aspirant...

for admission through the jee mains examination you will need to qualify the cutoff declared by the examination committee. The cutoff is not yet declared but as per the prediction s and the result analysis  the expected cutoff result is declared. you can refer to the link given below for the expected cutoff..

https://engineering.careers360.com/articles/jee-main-cutoff

hope this helps