A biographical article about Rev. Judson C Davidson, Pastor of Grace Baptist Church in Baltimore provides the following information about his family. He was born in 1849 and he married Lizzie Diugiud. It is stated that his ggg-grandfather came from Scotland and settled in America. The Rev.'s father, J T Davidson, born in Appomattox Co, Virginia, farmer, a leader in community affairs, married Martha Osborn. He died in 1886 at the age of 74. Children listed for J T Davidson besides the Rev. Judson were John W, T. O., Samuel, and Catherine who married J W Carson. J T Davidson's father was listed as Samuel Davidson. The article provided a few more details about the Reverend's life and the places where he lived.
Source: Digitized image of Genealogical And Biological Record of Baltimore. It is a large book that has been digitized and can be viewed on the Maryland State Archives website. It takes a long time to download in PDF format so be prepared for a wait. There is an index at the back of the book. His bio is on p. 788.
The father, J T Davidson, is the same as Jesse T Davidson. If the article is correct in terms of the generations, then it means that it was Samuel's grandfather who came over from Scotland.
This is not my line but hope it may help others in their search. It helps to narrow the focus somewhat. Many members of this Davidson line can be viewed in the Appomattox census records.