In his course on inferential genealogy, Tom Jones suggests that most genealogical questions come in two flavors, those of identity or relationship.
Rare is the case where early vital records of New England towns provide enough information that all by themselves, the information is sufficient to prove the identity and genealogical relationships of those whose records are there memorialized. We know the US census do not report about relationships until 1880; we don't even have a record of household member names until 1850.
The vital records and census provide clues; when considered with other records--tax, court, probate, burial, obituaries and news items, town records and histories, military records, etc.--the vital and census records often help solve the problem.
The premise of this question is that a man, Jacob Fisher (1776-1820) is the son of Jacob and Sarah (Hodges) Fisher.
Although limited resources are being observed, there seem to be some obvious inconsistencies between the premise and those (few) resources.
The vital records Fortiter provides show no record of a Jacob Fisher d. 1820. Indeed, the vital records of one Jacob Fisher report his death 1842, ae 66; suggesting he might be the man born 1776 to Jacob and Sarah (Hodges) Fisher.
See Almon D. (Almon Danforth) Hodges, Jr., compiler, Genealogical record of the Hodges family of New England, ending December 31, 1894 (1894), p. 173. Hodges provides an unsourced biography for Sarah5 Hodges (Josiah4, Henry3, 2, Wm1), b. Stoughton, 1754 or 1755; d. Sharon, 1792. Sarah reportedly m. 1773 at Stoughtonham (now Sharon), Jacob Fisher of Stoughton, son of David & Deborah (Boyden) Fisher. Various details about this Sarah (Hodges) Fisher including a details about her children: Jacob, Betsey, Sarah, Spencer, Abner, Thomas and Hannah. The son Jacob6 Fisher (who died at Sharon in 1842) said m. "Mary Witherton [?]"
- Same source, p. 117 has unsourced biography for Sarah (Hodges) Fisher's father, Josiah Hodges m. Mary Coolidge.
- Moreover, one published source reports that Jacob Fisher (1776-1842), son of Jacob and Sarah (Hodges) Fisher, with his wife, Mary Withington, had but one child--a daughter, Hannah. This daughter (Hannah) is said to have died unmarried in 1849, at about ae 50. See Charles Frederick Robinson, Weld Collections (1938), p. 96-97, reporting a biography for Samuel6 Weld. More details available from the source, but this Mary (Withington) Fisher is reported the granddauther of Samuel6 Weld by his daughter Hannah (Weld) Withington. Mary (Withington) Fisher reported b. 1777; d. Sharon, Mass, 1848; m. Roxbury 1799. Robinson provides various sources in the biography, but none explicitly for this grand dau. Mary (Withington) Fisher.
As with all sources, biographies are subject to error and omission. It is often helpful to learn if more current work is available. Likewise, to confirm the sources and discover inconsistencies yourself.
Updated: The profile Duncan provides for his Jacob Fisher (d. 1820), reports a death at Bolton, Worcester County, Mass. and a wife Ann Pierce (m. at Boston in 1803). See Bolton Births (Fisher), Bolton Marriages (surname Fisher) and Bolton Deaths (surname Fisher). The Jacob Fisher 1820 death record gives the wife's name (Ann), but doesn't provide his age at death. Just when this Jacob Fisher was born is not obvious from the records of Bolton, but the birth date in the profile seems to be that of the different man who was of Sharon.