"Big Jake" was introduced to the world in 1958 by Troxel descendant Thomas H. Troxel in a 45-page book called Legion of the Lost Mine. In his forward, the author admits to fictionalizing some of the characters.
About Big Jake's origins, T. Troxel writes that Big Jake was born in Philadelphia in 1757 "of Swiss parentage and had received his education in the city of independence and brotherly love. He enlisted in Washington's Colonial army when he was sixteen years old  and served nearly four years  during the Revolutionary War." (p 9)
Jacob Troxel's own testimony when applying for a military pension is that he was born in 1759 in Frederick Co., Maryland (not Philadelphia), and that he enlisted in 1777 (when he would have been about 20) in Loudon County, Virginia; his service in the war was on again, off again, and concluded his service in late 1781 after having marched to Yorktown, Virginia where Gen. Washington obtained the surrender of Lord Cornwallis. Some of that on again, off again service included time in Pennsylvania; none of it included time in Kentucky; per his own testimony, Jacob Troxel did not arrive in Kentucky until 1801/2.
Therefore "Big Jake" -- if he existed at all -- who supposedly married a daughter of a Cherokee chief in Kentucky before the conclusion of the Revolutionary War, could not have been this Jacob Troxel.