The Axe Soldier is an unused class in Fire Emblem: Genealogy of the Holy War. It is an axe wielding variant of the Soldier class.
In TearRing Saga: Utna Heroes Saga, the Axe Knight class seems to be heavily inspired by this unused class. The Axe Soldier proper appears in TearRing Saga: Berwick Saga.
In Fire Emblem: The Sacred Stones, by using the summon skill, you can summon an axe wielding phantom, which both its in game portrait and sprite resemble that of a deceased soldier wielding an axe.