Here's the other Fighting style I had came up with for my Fighter sub class. All of them were based on a specific skill. Not all of 'em are winners...
Beguiling Raven Style
When you inflict damage to a creature with a weapon attack, you can choose to make the damage equal to your Charisma modifier. If you do so, one ally who can see you within 20 feet of the target can spend their reaction to move their speed. This movement does not provoke opportunity attacks from creatues that can hear you.
Brutal Badger Style
When you inflict damage with a simple melee weapon or a sling, you can spend a bonus action to make an additional attack with the same weapon. When you use your Action Surge class feature to take the Attack Action, you can make one additional attack with a simple melee weapon or a sling.
Dancing Mantis Style
Once per Attack Action, when you inflict slashing damage to a creature with a melee attack, you can choose to use your weapon to also inflict slashing damage equal to your Strength modifier OR your Dexterity modifier to a different creature within 5 feet of you.
Eagle Eye Style
When making a ranged weapon attack while you do not have advantage or disadvantage, you can choose to impose disadvantage on your attack. If that attack hits, select either Strength, Dexterity or Constitution: the target of the attack has disadvantage on their next Saving Throw of the selected ability until the start of their next turn. A creature cannot be affected in this way more than once per turn.
Fell Scorpion Style
Once per Attack Action, when you inflict piercing damage to a creature, you can add twice your Wisdom modifier to the damage roll, but if you do so the target of the attack has advantage on their next attack roll against you until the start of your next turn. The creature cannot be an Abberaton, a Construct, an Elemental or an Ooze. In addition, you can apply a dose of poison to a weapon, consume a potion, or administer a potion, as a bonus action.
(posibly could be split into two? I dunno)
Howling Wolf Style
When you score a critical hit, or use your Action Surge class feature, one ally that can hea you can use their reaction to make an attack. This ally adds your Charisma modifier to that attack roll.
(Considering the Champion is a crit fisher, it's surprising there's nothing that triggers on a crit...)
Raging Ram Style
Once per turn, when you inflict bludgeoning damage to a creature that is no more than 1 size larger than you, you can push that creature 5 feet and then you can move 5 feet. This movement does not provoke opportunity attack from the target, and you must end that movement within 5 feet of the target.
Regal Lion Style
When you roll for initiative, add wice your intelligence modifier to your Dexterity roll. After you and all your allies have olled, but before learning the result of your enemies' initiative roll, you can exchange initiative result with one willing ally that can hear you.
I also had more advanced fighting styles (the Divine Styles) later on in the subclass progression. I tried to make four, based on what I imagine as the main four types of Fighters: Sword and Board, Big Whacking Stick, Twin Weapons and Archer. I got two out of four that worked well, but I still needed work. I think the most interesting one was :
White Tiger Divine Style
When making an attack, you have a +2 bonus to damage rolls made against creatures you have already attacked this turn and a +2 bonus to attack rolls when attacking a crature you have not attacked this turn.
The idea being that using two weapon fighting you'd constantly have to weight in the advantage of spreading damage or focusing your fire. And of course, it would conbine with whatever other Fighting styles you had previously picked.