It appears from the Princeton Vital Records, that the only son of Jesse an Abigail was Jesse born at Amherst, NH on November 3, 1782 and recorded at Princeton, Mass.
Jesse died intestate and his widow Abigail requested that Isaac Jones be appointed estate administrator on March 25, 1783. Case 10418:p. 1-14: Middlesex County, MA: Probate File Papers, 1648-1871
The note on his profile probably reflects the son Jesse.
It appears that Jabez, attached to Jesse Sr. is incorrect.