The following data is extracted from Genealogy and Biography of Ontario County, New York.
The Hornbeck family is of Dutch ancestry. Warnour Hornbeck was an early settler in Ulster county, New York. He married (first) Anna, daughter of Matthaus and Eva Abertse (Bradt) de Hooges. He married (second) Grietze Tyssen. By his two wives he had eighteen children and their descendants have been very numerous. Doubtless all of the name in New York are from this pioneer family. Lodwick Hornbeck, of this family, married, July 9, 1696, Maritze, eleventh child of Cornelis Cornissen Vernvoy and his wife Annatje Cornelis, daughter of Cornelis Barentsen Van de Cuyl and Lysbeth Arents. Lodwick and Cornelis Hornbeck were witnesses of the will of Cornelis Swyts, dated April 13, 1735, at Rochester, a town in Ulster county. In the Ulster county wills we find early mention of Cornelis, Gerardus, Isaac, Jacob, Jacob Jr., Johannes, Lodewyck. Philipa and Petrus Hornbeck.
James Hornbeck, doubtless a descendant of the Ulster county family, was born in Orange county, New York, where some of the descendants settled. He came to the town of Phelps, in Ontario county, New York. when a young man, and took up a plot of five hundred acres of forest land. He was a progressive and successful farmer. He married Margaret Burnett, born in Orange county, New York, Children: Wells, Charles, Bessie, Mary, Alvira, Ann, Jane. James B., mentioned elsewhere.
James B., son of James Hornbeck, was born in the town of Phelps, New York. July i5, 1827, and was educated in the district schools of his native town. During his long and useful life he has followed farming for an occupation and his business has proved highly successful. He commands the confidence and esteem of the community and is conspicuous for his public spirit. He is a member of Eureka Grange, Patrons of Husbandry, of which he was one of the founders. In politics he is a Democrat. He married, 1853, Phila M. Peck, born in Phelps, daughter of Hiram Peck. Children, born in Phelps: 1. Clara A., married John Jennings. 2. Ida P., married Anson Lay.
Source: Genealogy and Biography of Ontario County, New York