Amit, first of all, you will need to look that whether with your 56.2% in the 12th board you are in top 20 percentile in Bihar board or not because if you are in top 20 percentile then only you will be able to further sit in the JoSAA counselling for getting admission in different NITs and IIITs. If not then you will be disqualified because it is essential to have minimum 75 percentage in 12th board exam in order to be eligible for JEE Mains exam.

With your 4964 rank in the JEE Mains exam under SC category you can easily get admission in all the branches of NIT Patna with your home state quota and even you will have a good chance in getting into other NITs but as I said above first you need to check the eligibility status by checking whether you are in top 20 percentile or not because right now with 56.2 percentage you are not eligible for any further process of counselling.

Feel free to ask if you have any more queries. All the best!!