Pugilist

Pugilism, or the study of boxing, has a long and storied history in academia. Students of institutions of higher learning often dabble in Pugilism, which is colloquially known as the "Sweet Science". Arcane pupils are no different, and sanctioned boxing clubs can frequently be found wherever future Wizards congregate.
Some Wizards take their interest in Pugilism to the next level, and seek to incorporate the sport into their spell-craft. Offensive spells are delivered with heavy blows rather than delicate somatic gestures, and protective magic is woven into their stance.

Level 3: Pugilist's Stance

You have crafted a defensive posture that guards against both physical and magical attacks. You always have the Mage Armor spell prepared and you may cast once per Long Rest without expending a spell slot. If you cast the spell this way, you also gain a number of temporary hit points equal to twice your Wizard level. 

Level 3: Arcane Wallop

Pugilists have developed a special technique of delivering their offensive spells through magically empowered fisticuffs. Whenever you cast a spell that requires you to make a spell attack, you may instead make an unarmed strike. The target must be within your unarmed strike range. Using an Arcane Wallop to perform a ranged spell removes any disadvantage caused by having a hostile creature with 5 feet of you.

When you miss a target with your Arcane Wallop, you may attempt to recapture the expended energy. Using a Reaction, you can make an Intelligence Check, the DC of which is equal to 10 plus the level of the spell slot used to cast the spell. On a success, you do not expend the spell slot.

Level 6: Erudite Counter

At 6th level, you learn to exploit weaknesses in other spellcasters' stances. You always have the Counterspell spell prepared. Whenever you successfully cast Counterspell, you may also force the creature casting the spell to make a Constitution saving throw against your spell DC. On a failed save, the creature is knocked prone, and takes 1d8 psychic damage for each level of the countered spell.

Level 10: Mystic Haymaker

At 10th level, you improve the capabilities of your Arcane Wallop. When you cast a spell that forces a single target to make a saving throw, you can instead make an unarmed strike against the target. The target must be within your unarmed strike range. On a hit, the creature suffers the full effects of the spell, as if they had failed the saving throw. If you miss with this attack, the spell resolves as if the creature had succeeded on the saving throw. If the spell requires any additional saving throws from the target, those saves are rolled normally.

Just as with your Arcane Wallop, you can attempt to recapture the spell slot used on a miss. Using a Reaction, you can make an Intelligence Check, the DC of which is equal to 10 plus the level of the spell slot used to cast the spell. On a success, you do not expend the spell slot.

Level 14: Standing Six Count

At 14th level, you learn to quickly draw in magical energy to refresh yourself during combat. You may spend an action to use your Arcane Recovery feature, instead of needing to complete a short rest. When you do so, you may also expend a number of Hit Dice up to your Intelligence modifier (minimum of 1).