Conures fighting, need help...

[Conureflock]

So I have three conures, one black capped and two green cheeks (one pineapple and on yellow sided). I’ve had them well over a year and after being slowly introduced they all got along. Now for some reason really out of the blue, two of them can’t stand each other and fight.
Not just like a slap on the wrist it seems very aggressive and won’t stop until I’ve physically grabbed one and removed them from the situation. Even with throwing like a shirt over them, they’ll continue to fight, they’ll fight though my hands, on me, through cage bars! Luckily I’ve always been there as I decided to stop letting them out unsupervised so the worst injuries are small cuts on their feet, but I still don’t want any of them to be hurt.

Here’s my question: what do I do?!
If I have to supervise them to be out they won’t get as much time out as they deserve.
If I let them out in pairs I worry the separation will make them more opposed to one another.
I love all three and really really don’t want to part with any but at the same time I know this can’t go on. My only theory is that they’re maybe fighting over the other bird? I don’t know any of their genders so I don’t know how possible that is or whether birds do this?
Any advice would be great, anything to help them and avoid rehoming would be a life saver! I don’t want to think this is my only option, but I want to be a responsible bird owner.

Also, they don’t live together, they’re all housed separately.

 

[Laurasea]

Whoever was your first bird , if they are one of the fighters might need extra reassurance and attention.

Things change. Try doing flock observations, objectively. When I did this I found I had a different problem than I thought..

 

[Conureflock]

See my first bird is not one of the fighters and bless her (not sexed) she try’s to separate them. She seems to be the most social, I’m not sure if it’s a gender thing with the other two fighting over her??
She’s also quite good at dividing her time of late, she’ll spend a little while with one giving them some attention and play time and then the other and then me!

 

[Laurasea]

Aww.
This article is good , maybe you'll find something that helps.
https://lafeber.com/pet-birds/bird-behavior/