
Farnham is a village in the town of Brant in the southwest corner of Erie County. The Lake Shore and Michigan Southern (New York Central) and Pennsylvania Railroad had stations in the village. The Nickel Plate Railway also passed through town but I don’t know if they had their own station, shared the PRR station, or did not service the village.
Pennsylvania Railroad

Lake Shore and Michigan Southern Railway

The Buffalo and State Line Railroad completed its line through Farnham in February 1852. The line was later operated by the Buffalo and Erie Railroad (1857 – 1869), Lake Shore and Michigan Southern Railway (1869 – 1877), New York Central and Hudson River Railroad (1877 – 1914), and New York Central Railroad (1914 – 1968).
As of 1860, the Buffalo and Erie Railroad station in Farnham was known as “Saw Mill”.