Pre-nuptial agreements are common in the US. Having one is not of itself a problem in a green card application, nor in a marriage. Their existence is not published, nor made available to any government organization. Nor are you required to volunteer the information that you have one.
The answer to your cross-posted question on our Law site is very detailed and informative. It points a number of minor pitfalls that you should be aware of. None of them is likely to be a problem if your marriage and agreement are genuine and normal, and has been drawn up by a lawyer who is aware of your immigration plans.
If you are asked whether you have a prenuptial agreement (either on a form or in person in an interview) you must answer truthfully. Failure to do so is deception and can result in denial of immigration. I do not believe you are required to show it to an interviewing officer if asked, but you must remember that the onus is on you to prove that your application is legitimate, not on the officer to prove that it is not. If there is nothing in the agreement that makes it look like your marriage is a deal for immigration purposes you might be better off showing it to them.
To quote from the other answer:
If the agreement makes it appear that the parties contemplate that the marriage will be short-lived, and that an end to the marriage will occur in the near future, that makes it look like a sham marriage. If it appears that the prime reason for the marriage was financial, and particularly if the US party has apparently been paid or subsidized for entering into the marriage, that also makes the marriage look like a sham. If the terms of the agreement support either of these assumptions, that may cause a problem.
Also the agreement must not attempt to invalidate the legal obligation on the citizen spouse to support the non-citizen spouse (I-864), regardless of the continuation of the marriage.
Both parties must understand the nature of the agreement. This condition is unlikely to be a problem with a spouse who has been studying in the US.
For references to back this up see the linked answer.