He may be the John Remington listed in the 1800 Federal Census at Johnston, RI. If so, I cannot account for the individuals in the household, as there appears to be an extra girl (3 under 10) and a boy age 10 - 15.
He appears to be the John Remington living in Gloucester, Providence Co., RI, in the 1810 census: 1 male under 10 (William), 1 male 16-25 (?), 1 male 26-44 (John), 3 females under 10 (Susan, Sarah, Harriet), 2 females 10-15 (Lydia, Phebe), and 1 female 26-44 (wife Sarah). He is listed next to Caleb Remington.