Fort Clayton is not a place that has many traditions, but it is remembered amongst Panamanians as one of the places that was part of the Panama Canal Zone. So Fort Clayton has historical meaning to Panamanians. Every time you go there or just even drive through that area, it brings memories of the days when the Panama Canal Zone was still administered by the US army.
The people of Fort Clayton do not really celebrate US holidays, but since many Americans live there, you will see them go on picnics or go out and play football during American holidays. American football is a popular sport in Fort Clayton because of the people who live there.