 NY 368 began at an intersection with NY 321 adjacent to the Carpenter 's Brook Fish <unk> in the town of Elbridge . The route headed north as Halfway Road , passing by farmland as it headed through a rural area of Onondaga County to the small hamlet of Halfway . Here , NY 368 served a small number of homes as it crossed a <unk> railroad line ( now part of the Finger Lakes Railway ) at the center of the community . Outside of Halfway , the route turned to the northwest toward the village of Elbridge , avoiding a marshy area directly north of Halfway . It intersected with Lynch Road and Campbell Road before turning slightly northward and following Carpenter 's Brook through another undeveloped area to an intersection with NY 5 east of the village , where NY 368 ended . 
