College can sue you to recover college fees on basis of undertaking given by you 

Even if student quits the course you are liable to pay the fees 

they can sue you on basis of undertaking 

As per the guidelines set by the Supreme Court of India, here is the NRI quota eligibility criteria: One of the parents must be an NRI residing abroad. The person sponsoring the education must be an NRI residing outside India and a first-degree relation with the student.

As per the guidelines set by the Supreme Court of India, here is the NRI quota eligibility criteria:

• One of the parents must be an NRI residing abroad
• The person sponsoring the education must be an NRI residing outside India and a first-degree relation with the student
• In case of no parents/relatives, the guardian must be an NRI residing abroad and must treat the student like a ward backed up by an affidavit showing interest in the affairs and relationship with the student. 
• Nearest Relative can be defined as the real brother/sister of the parents, maternal or paternal grandparents, or first degree maternal and paternal cousins.

Besides;

the residential proof of the sponsor to be provided, i.e., Resident Certificate of sponsor issued by the embassy of residing and IT complying country;

identity proof of the sponsor namely Passport/ Visa/ Resident Visa;

Income proof of the sponsor namely PAN card/tax documents;

Thus the documents submitted by you would be sufficient to recover the money from you if you discontinue the sponsorship payment because you have already given an undertaking to this effect. 

If the student discontinues or the institution terminates the student then the institution will take appropriate action as per the rules and regulations of the institution or the terms and conditions mentioned in the admission form/prospectus.

If you are required to provide the details of your employment in the form of an affidavit or as an additional document then it will be clear that you will be pursued on the basis of the documents submitted by you. 

If you give on stamp paper then the same can be executed by college against you

- As per the Supreme Court order, the eligibility criteria for NRI seat aspirants are:

1. One of the parents of the student should be an NRI and shall ordinarily be residing abroad as an NRI

2. The person who sponsors the student should be a first-degree relation and should be residing abroad as an NRI

- Further, in case a student is taken as a ward by other nearest relative, then such students will be considered for admission if the guardian ordinarily resides abroad as an NRI and has a bonafide that authorizes the student as their ward and has shown interest in the affairs of the student and in the relationship with the student.

- Since, you are giving an undertaking for the payment of his fees , then you are bound with the terms of the undertaking leally , and the college can sue for the recovery of the amount and for taking admission on the NRI quota . 

- However, if the student quits the course , then the college cannot recover the amount.

-  It is well settled law that any service provider like the training institutes, educational institutes/schools or College /university cannot be allowed to forfeit the fees or consideration received in advance in case the student has not availed the service. 

In such cases the management insists on advance payment of course with discounts. Otherwise they take fee in advance for a year before hand. There is no question of pursuing you, as they will not you to keep arrears. 

When you sign an undertaking to bear the entire expenditure of your nephew's studies, it is considered a legal contract between you and the university. Generally, contracts are enforceable, and if you fail to fulfill your obligations under the contract, the other party (in this case, the university) may have legal recourse.

If you are unable to continue paying for the entire duration of the course, it may depend on the specific terms and conditions mentioned in the undertaking. If the undertaking does not specify any consequences for non-payment or breach of contract, it may be challenging for the university to pursue legal action against you or your assets.

However, if the undertaking explicitly states that you will be liable for the entire course expenditure and does not provide any provisions for discontinuation or inability to pay, the university may potentially pursue legal action to recover the unpaid fees. In such cases, it's important to carefully review the specific terms and conditions of the undertaking to understand the potential consequences.

Regarding the scenario where the student himself quits the course or is unable to complete or pass the exams, it would depend on the specific terms mentioned in the undertaking. If the undertaking only holds you responsible for the payment of fees, and there are no provisions regarding the student's performance or completion of the course, it may not affect your legal liability. However, it's crucial to review the terms of the undertaking to determine the exact obligations and responsibilities outlined.