"The Origins of the Yellowstone River" is one of the only verified and authentic native stories of the region. A Northern Shoshone man named Ralph Dixey told a version of it, and it was collected in 1953 by folklorist Ella E. Clark. Other than this story, there is little reliable info or documentation on legends, myths, or other native folklore about Yellowstone.

I highly recommend "Tales from America's National Parks: Campfire Stories" edited by Dave and Ilyssa Kyu. It touches on 6 national parks and has a section on Yellowstone but mentions native folklore and stories from each park which the editors said were hard to come by as someone else mentioned here that a lot of native stories were told by word and not recorded.