You are far away from U. S. Marshall's in Paris, TX being it was ten years later and west of Paris.
Now, I have written a manuscript biography on George R. Tucker who, was hired as town marshal [officially named constable] in 1878 or 1879. The town was wild as the Texas to Kansas cattle trail came just west of Spanish Fort. Of course, once across the Red River the trail became the "Chisholm Trail." Horse theft and whiskey running was the primary businesses around Spanish Fort.
I will check my files and see if your Green Jackson is listed. I doubt very seriously that a U. S. Marshal at Spanish Fort shot him. He would have been out of Judge Parker court in Fort Smith in 1879, so??
I will see if Tucker Id'd him and email you.