Hey this year due to the covid-19 situations prevailing in the country the JOSAA authority has decided to conduct the verification of documents completely online .The candidates are not required to report at the allotment centres the whole process will be conducted online and you can conduct your verification of documents by logging onto the portal . I advise you to do the step of verification at the earliest so that you don't feel any last minute issue.
To know more about JOSAA counselling , followthe given link:

https://www.google.com/amp/s/engineering.careers360.com/articles/josaa-counselling/amp

To predict the list of NITs where you can get a seat you can use JEE mains college predictor tool :

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer