Which among the following football competitions holds the distinction of being the oldest in Asia?

The correct option is Durand Cup.

Explanation:
1. Durand Cup: Founded in 1888 by Sir Henry Mortimer Durand in Shimla, India, the Durand Cup is the oldest football tournament in Asia and the third-oldest in the world.
2. Santosh Trophy: Started in 1941, it is a major Indian state-level football competition, established decades after the Durand Cup.
3. Subroto Cup: Founded in 1960, it is an international inter-school football tournament.
4. Federation Cup: Established in 1977, it was an annual domestic knock-out football tournament in India.

Thus, the Durand Cup holds the distinction of being the oldest football competition in Asia.