Court records show that Jesse, Senior, did not draft his will until 1802 and it was not probated until Nov 1808.
As to Jesse, Junior, it appears to me that he and his family were in the 1800 census household of Jesse, Senior. I do not know when Jesse, Junior died, but the first record I have found specifically identifying his wife as a widow was in 1813. Another record a few months earlier in that same year names her and Capt. John CARROLL--very likely his brother--as administrators of the "the estate of Jesse Carroll decd."
Would you please tell me how you KNOW that Jesse CARROLL, either Senior or Junior, died in 1801?