I am assuming he is the Willie Wells age 5 in the 1880 census with his grandparents at Lorraine, Jefferson Co., NY.
In 1900 William Remington is age 26 and married. His grandmother Amanda Remington is living with his family at Boylston, Oswego Co., NY. I have made an assumption that his mother is Eva.
I am also assuming that Willie Wells and William Remington are the same individual. As far as I know, Orsemus & Amanda had only one daughter. It could be that Willie was born to Eva before she was married, or that she was married only briefly.
In the Federal Census of 1930, William J. & Mary A. Remington, ages 55 & 52, are living at Lorraine, Jefferson Co., NY. With them are Samuel E. 25 and Eva D. 22. Living nearby are Harold and George and their families.