I do not recall any legend or folk lore of this immediate section of New Mexico. Of course, you are familiar with the Saga of Billy the Kid as told by the romantic and heroic writers, in whose writings there seems to be evidence that Billy the Kid was not killed by Pat Garrett, but that he lived to be an old man down near Marfa, Texas, and died only a few years ago.
There are three, reasons why so many people think that he was not killed, one is that his sister came out to see him and then did not go to his grave, but went directly east. That his horse was never seen again, is another reason. Third, is that Pete Maxwell and Pat Garrett were his friends, and that a Mexican was buried instead of Billy the Kid, and that he, Billy the Kid, went down in Texas on the Rio Grande.