Triton's surface is covered with mostly frozen nitrogen. a mostly water-ice lower crust lies beneath, with an icy mantle and a substantial core of rock and metal deeper down recalling the constituents of the triton's atmosphere, what is the most likely mechanism that maintains tritons atmosphere?

Recalling the constituents of the Triton's atmosphere, the most likely mechanism that maintains Triton’s atmosphere is the sublimation of the surface ices. When the surface ice directly turns into water vapor without first transforming into liquid, this is what is referred as “sublimation”. Any solid that turns into vapor without having to chase its phase to liquid can be said to sublime.