I have compiled all of your and your mother's comments/questions from multiple threads. I put the information into manual family group sheets in an attempt to untangle the information and answer some of the questions.
First, there are several conflicting bits of information that have been posted. As I went through the comments, I had to cross out previous information I had written down that was posted because it was different. An example is that in various posts, your mother names the same woman as her mother, her grandmother, and her adopted grandmother.
Second, it would likely benefit your research efforts if all of the comments/questions are in the same thread. It makes it so much easier to help someone when you can scroll up and see all the information and reference the search efforts that others have offered. Otherwise, every person who wants to help is starting from scratch with information.
Third, your mother stated on another thread that she believes there is Native American ancestry in the family and believes that the number you referenced above is an Indian roll number. The number above which you asked about is NOT a Native American roll number; it references the format which the state of Texas used to record birth records. After your initial post, I was able to duplicate your research efforts and locate the record you were referencing.
Why does your mother believe there is Native American ancestry? If your mother is not certain of the identities of her biological parents, I am unclear why she believes they have Native American heritage. While there is certainly the possibility that she has a Native American in her family tree, it is imperative for you both to know that "having an Indian ancestor" is the MOST COMMON genealogy family myth. When it is true, it is nearly always much further back than people realize and the ancestor is usually only a small part Native American.
I searched the Native American rolls and could find no record of a Disheroon, Dishroon, or similarly spelled name. On all records I found for your family, they are repeatedly referenced as "white." It is important to note that in many of these documents, they weren't self-reporting the information; the record keeper would make the racial determination based on appearances. Obviously, appearances are not always what they seem, but I wanted to be sure to point this out because people often counter that fact with stating that the ancestor would have "wanted" to be recorded as white, so they would have reported that they were if they could "pass." In most cases, it wasn't up to the person, but rather to the record keeper to record someone as white, black, etc.
If your mother is curious about her biological parents, then the best approach to take is to engage in traditional paper trail genealogy research as well as DNA testing. This will also most likely help answer questions about Native American ancestry. In MOST cases of U.S. Native American heritage, if there is adequate and recent (both of those are important) Native American DNA, it will show on a test. Particularly if multiple DNA databases (more than one company and GEDmatch) are utilized. My DNA showed much more Native American than I expected, and I knew how far back it was. My point is, if the ancestor had more than a little Native American heritage and was in the last few generations, it nearly always shows in DNA. I can't speak to other lines in your tree, but there does not appear to be any Native American in your Dishroon line in the last 150 years.
There are many of us who would love to help. That is why we post in these forums. Personally, I've been volunteering in genealogy research for several years in various places. Many people would love to help the two of you, and I've seen many offers and attempts in the various threads from which I compiled the information. In order for people to help, we need to be able to understand what is being asked, what you both know, and what records you already have.
Best of luck.