Hello Aspirant,
According to the category rank you have mentioned in the question you have no chances of getting CSE branch in NIT Patna even under Home state quota as per previous year's cut-off. As cut-offs for this year is not declared yet so we can guide you on the basis of previous year's cut-offs which are given below :-
For complete details about previous year's cut-offs refer the link given below :-
https://engineering.careers360.com/articles/jee-main-cutoff-for-nit-patna
Note that the cut-offs are bound to change every year depending upon various factors, so to get an idea we can use last year's cut-offs.
However I would recommend you to use JEE-Main College Predictor to predict the chances of your admission in different colleges based upon your percentile and category :-
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
I hope this information helps you.
Good Luck!!
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