Anna Lee Day was my grandfather's sister. Oscar E. Day was also born in DeKalb Texas. To my knowledge none of them were Texas Rangers, although I have heard that they had an Uncle Daniel Day who was a Ranger. Uncle Daniel's family was last found in the 1920 census of Waxahachie Texas his wife Georgie a widow with several daughters.
Daniel Day and his brother William Jasper Day came to Texas from Alabama in the early 1870's I believe they came with their Uncle John Hare Day in a wagon train. They first settled in Freestone County Texas.
I hope we can exchange more information.