I do not have names any of Julius Levi Ainsworth's children that were born after 1930. You say your grandfather was born about 1931 or 1932 and his father's name was J. Levi Ainsworth from Smith Co. That would be the Julius Levi I mentioned. Here are the children of Julius Levi Ainsworth that I have: Allief. b. abt 1916 Rachaelf. b. abt 1918 Ulius R.m. b. abt 1921 Elizaf. b. abt 1923 Bonnie J.f. b. abt 1924 Tommie L.f. b. abt 1926 Claudia M. f. b. abt 1928 These are all listed in the 1930 census. Any of these sound familiar?
As you can see, I have only one male so your grandfather would be the second male, there may be others born after 1930. Do you have your grandmother's name? I would like it if you have it.