Hedge Magic

While your latent magical talents are potent, you have not stuck to your coursework and your skills are less honed than other wizards. As such, you have failed your wizarding apprenticeship and in turn, rejected traditional arcane schooling. Now, you use your spare time to practice self-taught magics and further advance your skills.

Ad-Hoc Spellbook

At second level, your spell book has become a mess of spell derivations, notes, and failures. You can only prepare a number of spells equal to half your wizard level (rounded up) and you only learn one wizard spell per level gained. However, the gold and time you must spend to copy a spell into your spellbook is halved. You also learn one additional cantrip from any classes' spell list and you can select one 1st level spell from your spell book which becomes a cantrip for you. These spells do not count towards the total number of cantrips you know. When you gain a wizard level, you can change the 1st level spell selected to another 1st level spell from your spell book.

At 10th level, you can cast the 1st level spell selected as if you were using a 2nd level spell slot, if the spell has the ability to be cast at higher levels.

Practiced Formulation

Starting at 6th level, you practice creating spells has given you the ability to infuse your magic into sheets of parchment. After a long rest, you can use your spell slots to create up to 2 spell scrolls. The spell slot used is equal to the level of the spell selected. You must use a spell from your spell book and you do not regain the spell slot used in this manner until the associated spell scroll has been used and you have finished a long rest. The spell must be of a level equal to or below your proficiency bonus. The scroll does not require the spell's material components to transcribe or cast it. 

Spell scrolls made in this way are legible to anyone you choose and use your spell save DC and spell attack modifier.

Tenacious Casting

Learning your magic in the wilderness, instead of a more controlled environment, has made your more adaptable in combat. Starting at 10th level, you can add your Constitution modifier to your spell save DC. Additionally, when you are forced to make a Constitution saving throw to maintain concentration on a spell, you can use your reaction to add your Intelligence modifier (minimum 1) to the result of the roll.  

Improvised Barrage

You become adept at casting spells on the fly. When you reach 14th level, you can cast any cantrip you know, including the ones from the Ad-Hoc Spellbook feature, as a bonus action.