New York State Route 10 runs north-south in Western Montgomery County. It runs from the Montgomery/Fulton County Line, near Ephratah, to the Montgomery/Schoharie County Line, near Ames. NY St Rt 10 passes through the following towns in Montgoermy County. Palatine Bridge Canajoharie Ames NY St Rt 10 is multi-plexed in Montgomery County. New York State Route 5, at Palatine Bridge. NY St Rt 10 intersects the following highways in Montgomery County. New York State Route 5, at Palatine Bridge.