As an example, let's say someone with 1/16 of African American heritage applies for a minority scholarship at a US university. Can the university then proceed to sue the scholarship recepient on the basis of deception? If so, is there a US law which defines what constitutes belonging to a certain race or ethnicity?
Even if you're a white guy, you could get a report from 23andMe and you'll probably find out that you have at least 1/100 "African American" heritage.
The way America is now (and especially the university system) it is more relevant what you "identify as" than what you are.
What exactly is the wording on the scholarship application form? If it says "Do you identify as African American?" then feel free to say you do. In this case, the contract is clear that what you identify as is what is important.
If the application says "Do you have at least 50% African DNA?" and you lied about it then they could sue you, but I doubt that's what it says.
So check the wording and if you answer truthfully, they can't sue you. What you "identify as" is completely up to you.