Executions often use special flat blades, designed to remove the head of someone deemed guilty. To use one on the battlefield could be mark of foolishness, or, a declaration of where the enemy is planning to strike. 

Execution Proficiency

When you choose this archetype at 3rd level, you gain proficiency in executioner's swords. For the purposes of magic items or other effects, you may consider them longswords. However, while you wield such a weapon, it's weapon mastery is upgraded:

Beheading: When you roll a 20 to hit a creature with this weapon, roll the weapon's base damage die 3 additional times

Armor of Faith

Starting at 3rd level, your intensity fuels your faith. Often, the swords of Executioners had holy text written on their blades, giving prayer to those slain. As a part of the rites to become an  Executioner, the armor you use, along with your blade, are marked with these phrases. Choose a text from a holy book that has meaning to you, and to your purpose. Whenever you speak that line aloud, it activates your sword and armor, as if using a command word. It stays activated this way for one minute. 

While your armor is activated, you can use non-weapon items as a bonus action, including magic items that require a magic action, potions, and grenades. You also do not need a free hand to do so. 

While your Blade is activated, the Versatile trait (two handed) becomes 1d12

Rites of the Righteous

Starting at 7th level, you learn the canticles and rights when putting the guilty to death. You can use an action to chant these lines, choosing a creature you can see. During your next turn, you can treat the creature as if it were prone, and your attacks deal four times their usual damage to that creature. If you land a critical hit, the damage is instead ten times the usual. However, you can only make a single attack roll, regardless of the amount you could usually make. 

Pursuit of Justice

Starting at 10th level, when you use the last of your movement, and end without being within reach (with your weapon) of a hostile creature, you can use your reaction to move an additional 30ft. if your weapon is activated, and Rites of the Righteous is activate this turn, your attack this turn can ignore reactions that would change armor class or reduce it's roll or damage dealt. 

Heavy Hand

Starting at 15th level, you learn to maximize the use of your special blade. It's design is meant for granting a clean death to a criminal in chains. As such, when you attack a prone creature for the first time on a turn, you may roll two additional hit die. However, you cannot gain any additional die rolls, or use rerolls when using this feature. 

In addition, you can replace one of your attacks when using the attack actions to make a non-attack action:

Tank Shock: If you moved your full movement this turn, you may slam into the enemy. They make a strength save (DC 10+STR+PROF), or take 1d6 bludgeoning damage for every fighter level you have)

Mat Slam: if you moved your full movement this turn, you may drop the enemy to the ground. They make a dexterity save (DC 10+STR+PROF), or fall prone

Battlefield Templar

Starting at 18th level, your faith can shield you from the most grievous of wounds and snares. While your armor is activated, your walking speed cannot be reduced lower than 30ft, and you have resistance to damage not rolled in dice (flat damage).