The route was assigned in the 1930s and removed in 1980 as part of a highway maintenance swap between the state of New York and Onondaga County.

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 Conrail railroad line (now part of the Finger Lakes Railway) at the center of the community.

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.

[2][3] It remained unchanged until April 1, 1980, when ownership and maintenance of the route was transferred from the state of New York to Onondaga County as part of a highway maintenance swap between the two levels of government.