He lived in Cranston, RI; Grafton, MA; and Rehoboth, MA.
In the 1830 Federal Census, Jeremiah is at Grafton, Worcester County, MA.
Jeremiah is not mentioned in his father's will.
From Rehoboth, MA, Vital Records at newenglandancestors.org:
1845 REMINGTON Jeremiah, of Joseph and Alcey, buried Fall River, 58y 0m 8d, Sept. 22, 1845 8 2 Death
An individual named B. Chase has contacted me with additional data differing from mine concerning Jeremiah's parentage, so this may resolve some of the questions which remain (still needs more research).