Economic status is determined on the income of the candidate, not on the income of parent/s. He will still be entitled to claim 2B category. 

1)government allowed a 10% quota in government employment and educational institutions for the Economically Weaker Section of the general category.

2) To be eligible for the Economically Weaker Sections (EWS) category, a candidate must belong to the general category (not SC, ST, or OBC) and have a family income below ₹8 lakh per year, with specific restrictions on land and property owners

3) your low income status does not get changed 

Your sister is reportedly holding BPL card.

Households with an aggregate annual income less than Rs. 24,200 have been categorized under this group.

As on the date of application, if huas income or your sister's family income was under the criteria of BPL limit then this additional income added to the family by inheritance at this stage would not be considered as a disqualification.

Your sister's ₹20 lakh share from property sale won’t affect her son's NIT admission under 2B category, as eligibility is based on annual income, not one-time receipts. However, confirm with local authorities if needed.

Since he scored 95.6 percentile in JEE, he has a strong chance for NIT admission.

For detailed, personalized advice, consider a phone consultancy. Hope you find the information helpful. You are free to contact me for further discussion. If you could spare two minutes of your time to write a review, it would be greatly appreciated and bring immense happiness to read it. Thank you. Shubham Goyal.

No it will not affect his possibility 

- Since, she has got the said amount from her share in the property of her deceased father-in-law , then this will not considered as her income 

- Hence, this will not have any impact on her said category and her sons career will also not effected from gaining this fund. 

- Under BPL,  a household must earn less than Rs. 27 per day

Dear Client,

The BPL (Below Poverty Line) and 2B categories (backward class) are normally determined by annual family income, not on one-time receipts. Your sister's receipt of an inheritance or proceeds from the sale of property for ₹20 lakhs is a one-time receipt, so it may not immediately cause any problems for the 2B category for her son. Some schools and state governments may make a determination based on total wealth or total assets when determining income eligibility. I recommend checking the relevant criteria from the NIT or the state's OBC/2B category criteria. You could consider consulting a local revenue office to verify whether their one-time receipt of ₹20 lakhs results in the ineligibility for reservations.

I hope that helps. Do not hesitate to reach out for any further questions.

Money she is receiving as a one time settlement from sale of her father-in-law's house cannot be treated as her income for the purposes of categorising her income group.