This family group is in the 1860 and 1880 Federal Census at Ashford, Cattaraugus Co., NY. Bela was Justice of the Peace at Ashford in 1868.
In 1860 and 1870, there is a son Arthur living with Bela & Silphina, but in 1880 he is married; with Arthur at that time are Joseph & Loraette Remington, listed as his parents. So, I am assuming Arthur is Bela's nephew, a son of Joseph and a possible first wife.
From census data, it appears that his brother Joseph and sister Patty are also residing at Ashford.
In the Federal Census of June 1900, Bela & "Claphine" are still living at Ashford. Daughter Clare, age 26, is with them.