I like this quite a lot. I like how it gives "superiority dice" to the barbarian in an interesting way. Assuming you attack roughly every round, and crit about as often as you spend a round not attacking, you basically can spent 1 momentum die per round. That's +1d4/1d6/1d8 damage per round, which seems about right, when compared to what Frenzied Berserkers can do with bonus attacks.
Some quick feedback:
For starters, you need at least 1 sentence of flavor-text at the beginning, to tell us what the archetype is about. Otherwise it's hard to know whether the game mechanics are doing justice to the story. I gather from the mechanics that this archetype is about bouncing around the battlefield smashing people super hard (which, mechanically, is one of my favorite archetypes) but it's unclear what kind of person would do this.
Also, if this class is meant to involve a certain amount of movement, I think it needs some way to avoid taking opportunity attacks, or reduce their damage. Consider a maneuver that said something like: "Until the end of your turn, whenever you hit an enemy with a melee attack, you may push them back a number of feet equal to the roll of the momentum dice you spent." As long as you roll a 5 (the average of 2d4), that's going to prevent OAs from most foes (you can push a target with an attack, then run over and hit someone else). You could actually combine this with one of the weaker maneuvers, like the one that gives you bonus movement speed (because if you are planning to zip around the battlefield you'll probably want to shove people out of your way to avoid OAs).
Fearsome: ... On a failed saving throw, the foe becomes frightened for a number of rounds equal to the result of the momentum die spent.
It would be nice for the size of the momentum die to matter, but in 5E, we don't typically count duration in "rounds." It's just too easy to lose track. "Wait, was that 4 rounds, or 5? I think I forgot to update my dice-counter last round."
Parry: ... subtracting the result of those dice from the damage done.
Barbarians already have a ton of ways to tank. They don't need one more. It also seems like it doesn't fit with the subclass design, which otherwise seems very focused on damaging, hurting, and mangling your opponents; I think it's fair to say a subclass that gets a bunch of extra offense doesn't need more defense, too
Unfettered Aggression: When a creature enters the area you threaten, you can spend two momentum dice and your reaction to make an attack of opportunity against it. When you move close enough to an enemy to make a melee attack against it, you can spend two momentum dice and your bonus action to make one melee attack against it.
This is cool, but it sounds like two separate maneuvers: one as a reaction, one as a bonus action. I also think I'd reduce the cost to 1 or more dice, and if you hit, you roll the dice and add to damage. (That's a bit worse than Brutality because if you miss you've spent the dice -- but it's substantially better because it gets you an extra attack as a bonus/reaction -- but it can only be used in certain circumstances.)
Debilitating Strike: As an action, you can spend three momentum dice to make a single attack roll ... On a failed saving throw, you inflict an injury on the enemy that lasts until the end of its turn.
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This is very expensive, for an effect that only lasts until the end of the creature's next turn, and which will probably not work (you have to hit with an attack AND your foe has to fail a save). I'd consider combining this with Throat Punch. Maybe add Head Injury for some mental saves. One idea for making this cheaper/less complex: instead of expending momentum and requiring a saving throw, just make the injury automatic if you score a critical hit. Also look at the Open Hand monk's "Open Hand Technique" for a model; maybe the debilitation could be a rider on some other maneuver, like Brutality. (E.g., "When you use your Brutality maneuver, the victim must make a Con save, etc. etc.") Monk's Stunning Strike may also be a good model.
I guess my point is, at the cost of 3 momentum dice and your Extra Attack, this move only makes sense if you're setting up a spellcaster to put the whammy on your target with a Dex, Str, or Con save spell. That's pretty rare, and combined with the double chance to fail (miss attack and successful save) makes this ability very unattractive to me. Even if this cost 0 momentum dice I probably wouldn't use it.