I don't know for sure if this Joseph belongs in this family group, but the birth record identifies him as Joseph Remington, of Thomas. I have checked the family groups of the other families in Warwick, as well as the 1790 census for each of them, and Joseph fits best here.
An inventory of the estate of Joseph Remington of Warwick is listed in the probate records, viewable at ancestry.com, 13 Apr 1835; Thomas Holden, his guardian.