You can opt for the JoSAA counselling and counselling in private engineering colleges but before that you should have a clear idea about which of the colleges you have high chances in getting an admission.

Try tallying previous years' cut-off based on your Category, Home state, the department of your choice and then choose your preferred list of colleges in the JoSAA counselling. The process is quite hectic so if you want to ease it you may use our college predictor tool for knowing which colleges you might have a high chance of getting an admission in.

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

Hope this helped.