The Fortress Guard is a squad of military dwarves who take care of justice within a fort. Headed by the Captain of the guard, they are otherwise identical to your standard military squads, and can be treated as such.
 Selecting Guards
As this squad will be used to enforce justice and deliver beatings, it is good idea to select dwarves that are weak and unskilled in offensive combat. Basically, the exact opposite of a good candidate for a proper military squad.
 Equipping guards
It is important to equip dwarves with weapons as an unarmed guarddwarf can easily kill a peasant by suffocating him.
Training weapons or adamantine hammers along with low-quality wooden shields from light materials like feather tree wood solve this, but also make the guards mere meatshields that can't deliver a killing blow when attempting to use them to fight-off invaders.
Guards will train in barracks as any other squad, so it might be wise not to assign barracks to this squad, to keep fighting skill low and therefore make beatings less brutal.