Here is some information I found on Ada. Apparently it was born mainly with the expectation of being on the railroad route, but then they decided to build the railroad elsewhere.
This is the only Ada Texas I have ever been able to find, so I have to assume this is it. The timeframe would seem to work.
ADA, TEXAS (Nolan County).Ada was on Farm Road 1809 east of the Atchison, Topeka and Santa Fe Railway and north of Lake Trammell; the site is eight miles southwest of Sweetwater in central Nolan County. In 1897 Irving Wheatcroft, a railroad promoter, persuaded the citizens of Sweetwater to finance the construction of the Kansas City, Mexico and Orient Railway to link up Sweetwater with other lines to the south. The railroad was soon built to a point eight miles southwest of Sweetwater, and the new community laid out at that site was called Ada, after Wheatcroft's stenographer, Ada Cooper. The building of the railroad was delayed by financial difficulties, and the community developed slowly. In 1900 the owners of the railroad removed the rails and used them for another project, and when the railroad was eventually built later in the decade it was laid out to the west of Ada. Ada Common School was built in 1899, and by 1904 it had one teacher and twenty-two pupils. In 1914 Lake Trammell was built to south of the community. By 1940, when the site was identified on maps as both Ada School and, a little to the west, Lake Trammell, it had the school and scattered dwellings. The school was consolidated with the Sweetwater schools in 1941, and the site was deserted by the 1980s.
BIBLIOGRAPHY: E. L. Yeats and Hooper Shelton, History of Nolan County (Sweetwater, Texas: Shelton, 1975).