This is meant to be a short post so I'm not even going to go into any of the explanations about the "Indian princess" story. If you've heard it in connection to your family, read on. From November 1st to 15th, Fold3 is offering free access to their Native American Collection. If you really have Native American ancestry that's great but even if you don't, you may find valuable genealogical information in this collection.
You can read more details about the free access on Fold3's blog, https://blog.fold3.com/free-access-to-the-native-american-collection/. They also have great information about each collection (browse the collection rather than searching from the home screen to see this information). This will help you understand what should be in the records.
Much of the Native American Collection is only useful if your ancestors were Native American or interacted with nearby tribes. The main exception (because of volume of records/names) is the "Eastern Cherokee Applications." Read the information on the main page for that record group for full details about what they are and when they were created.
The short version for many southerners is, if your ancestors thought they had Cherokee blood, they may have applied to be enrolled as Eastern Cherokees in the early 20th century. Most applications were rejected but that has no bearing on whether the genealogical information is correct.
If you've heard the Indian princess story in your family, a relative may have an application in this collection, probably several relatives. The applications asked for information on the entire immediate family of the applicant (the applicant, spouse, their children, the applicant's parents, siblings, and all four grandparents). Not everyone filled out all of this information but some did and some gave even more than was asked for. You don't know until you check.
Also, you need to check for all the applications made by relatives. In my family, only one of my direct ancestor's applied. Lots of cousins, aunts, and uncles did, though. Some of them provided enough extra information that the information is about my direct ancestors. You also want to find every related application to see if relatives gave conflicting information. Much of this information is from oral tradition, not personal knowledge. People don't always remember correctly.
Try a Google search to learn more about using the Eastern Cherokee Applications (these are the applications for the Guion Miller Roll so some information will be found by using that as your search term). The Fold3 collection is not every name searchable because most applications are filled out by hand. The applicants' names are all searchable and typed documents will give OCR results. There's much more information available about the Eastern Cherokee Applications and related records than I can fit in a brief post. If you find some applications of interest, you may need to learn more to tease out further information. I've found dozens, if not hundreds, of applications for (mostly distant) relatives. I don't have any Native American ancestry.
Even if you don't find details about your ancestors, you can also use these if you are tracing descendants (say for a DNA study). You've got two weeks of free access to try this collection out. Get started.