Do you know when your grandfather died?There is a listing on the Social Security Death Index for James Quattlebaum, born 12 November 1896, died May 1963, Social Security Number issued in Florida.The record is here: https://familysearch.org/pal:/MM9.1.1/J2JY-WJ4
In the 19th and 20th century both birth dates and the spelling of names were rather fluid, and could change in various listings.
If you think that the James Quattlebaum from the Social Security Death Index could be your grandfather, then there are two census entries that could be of interset to you.
In the 1900 census of Precinct 21 Newville, Henry, Alabama the following household appears: Household Gender Age HeadR B SmothersMborn April 1852 Alabama SpouseNancy SmothersFborn February 1853 Alabama ChildMartha QuadebaumFborn July 1870 Alabama Grandson Alto QuadebaumMborn Jul 1891Alabama Granddaughter Fannie QuadebaumFborn October 1892 Alabama Grandson James QuadebaumMborn November 1896 Alabama Grandson John QuadebaumMborn October 1899 Alabama Grandson Walter QuddlebaumMborn June 1898 Alabama ChildWillie SmothersMborn March 1884 Alabama ChildJay SmothersMborn May 1886 Alabama The 1900 census record is here: https://familysearch.org/pal:/MM9.1.1/M98P-5HW
In 1910 James is still living with his grandparents at Newville, Henry, Alabama: Household Gender Age HeadRas B SmothersM 60y SpouseNancy SmothersF 58y ChildLettice KirklandF 30y Grand daughter Nettie KirklandF 12y Grandson Early KirklandM 7y Granddaughter Fannie QuartlebaumF 17y Grandson James QuartlebaumM 14y The 1910 census is here: https://familysearch.org/pal:/MM9.1.1/MKQG-VJ2
By 1920 James is married and has a child.They are living at Bay County, Florida: Household Gender Age HeadJames B QuattlebaumM 22y SpouseMargret QuattlebaumF 21y ChildLorene QuattlebaumF 5y born Alabama The 1920 census record: https://familysearch.org/pal:/MM9.1.1/MNYW-J6D
By 1930 the family has moved to Dunedin, Pinellas, Florida, and there are two more children: Household Gender Age HeadJames B QuattlebaumM 32 SpouseMaragret A QuattlebaumF 32 ChildLorene QuattlebaumF 16 ChildIris QuattlebaumF 7 born Florida ChildJames QuattlebaumM 5 born Florida 1930 census record: https://familysearch.org/pal:/MM9.1.1/SBF3-4ZM