Some wizards focus deeply on their capabilities within a particular school, eschewing study on certain others (which make no sense, and do not merit real study). These wizards tend to be enthusiastic about the study and effects of their school of magic, and downright insulting to .. certain other schools.
Since you began your studies, you have been interested and focused on the potential within some particular school of magic. When you select this archetype at 2nd level, choose one school of magic as your specialty, and two schools of magic that you oppose - choose from Abjuration, Conjuration, Divination, Enchantment, Evocation, Illusion, Necromancy, and Transmutation.
The gold and time you must spend to copy a spell of your specialty school are halved, and the gold and time you must spend to copy a spell from an opposed school are doubled.
Select one additional cantrip, which must be from your specialized school of magic, but can be from any class's spell list. This spell counts as a wizard spell for you.
During any short rest, you may spend 10 minutes with your spellbook and replace any number of spells that you have prepared from your specialized school with other spells from that school that you know.
Beginning at level 6, all spells cast from your specialized school of magic are cast as if you had used a spell slot one level higher than you truly used. This does not allow you to cast a spell with a slot below that spell's level. Additionally, when casting a spell from your school using a spell slot, you regain a spell slot two levels lower that has already been spent.
Unfortunately, your studies of your opposition schools have been neglected - any spell cast from one of those schools spends a slot one level higher than it would need to otherwise, and does not receive any benefit from doing so. As an example, if an Abjuration Specialist (who abhors evocation) wanted to cast a fireball, she would need to use a 4th level slot to do so, and it would still be cast as a 3rd-level fireball.
Once you reach 10th level in your specialization, you gain an incredible ability to focus on spells in your chosen school. Your concentration on such a spell cannot be broken by taking damage, and any attempt to counter or dispel those spells has disadvantage on any required skill checks.
Additionally, you can perform rituals from your chosen school in only two minutes instead of 10.
At level 14, choose one of these metamagic options from the sorcerer class:
If you choose an option from this list, apply its effects to every spell you cast from your school of magic (but using Intelligence where it says to use Charisma): Careful Spell, Distant Spell, Empowered Spell, Extended Spell, Subtle Spell.
If you choose an option from this list, you may apply its effects to a number of spells from your school of magic equal to your Intelligence modifier, and you recover all uses during a long rest: Heightened Spell, Quickened Spell, Twinned Spell.