Path of the Spell Blood

Your rage is so potent it has begun to awaken innate magic in your blood. Be it from an ancient dragon, tricky fae, or a powerful fiend or celestial, you have a magical potential similar to a sorcerer, but can't control it due to your tendency to lose control. Because of your lack of control you can't control how your magic takes effect when you rage, maybe you summon magical creatures to fight by your side, maybe your movements become hastened, or another creature slows down, the possible outcome seems mostly random. 
A barbarian who accepts the magic in their blood gains great power and advantages during a rage, however, such untrained magic is not something anybody could control or manipulate to a meaningful degree, and seems largely random similar to wild magic, though not to the same degree.

Spell Rage

Starting when you choose this path at 3rd level, when entering rage, you can choose to expand an available spell slot. You select a random concentration spell to take effect and have it apply to a valid target. Losing concentration on this spell does not stop your rage. When your rage ends, you suffer one level of exhaustion.

Rage Spellcasting

Starting at 3rd level when you select this path you may select any spells that require concentration from the sorcerer spell list. These spells will activate only while in rage.

Resistant Rage

Beginning at 6th level, you gain advantage on saves against spells and magical effects while raging and concentrating on a spell.

Improved Spell Rage

Beginning at 10th level, You gain the ability to either choose, rather than having a random spell active, or have two spells activate when you enter rage by expending a second spell slot, however activating a second will result in an additional exhaustion when your rage ends. Losing concentration on one effect means losing concentration on the second effect also.

Magical Feedback

Starting at 14th level, When you are hit by an attack or spell attack while concentrating on a spell(s) you can use your reaction to deal 1d8+your proficiency bonus psychic damage to the attacker after damage is dealt. Alternatively if the attack would cause you to lose concentration you may instead use your reaction to make an attack with a weapon you're holding in your hand that deals and additional 1d8+ your proficiency bonus+ the combined spell level(s)