How big is your tank?
How much water circulation do you have in your tank?
Anthias have a strict pecking order amongst themselves and are territorial in the wild.
If you have a smallish tank it will make the situation worse.
I think there is nothing much you can do. Let them trash it out and peace will return when they have established a pecking order.
Just ensure that they all get ample food (some anthias need to be fed multiple times a day).
In the wild, they are usually found in reef crests where a LOT of turbulent movement exist. They spend a lot of time and energy just staying above SPS coral heads which is their home, rather than fighting (as much as seen in captivity).
From my observation of them in the wild... I see that they peck at each other, even when swimming esp. the alpha males towards the lesser males and the females.
In my tank, with turbulent water movement, there is similar traits. When water circulation is stilled... they do chase each other more often.
The fathead anthia is a deepwater shy fish. They will get bullied by most fishes. You have to ensure they get enough food by target feeding them or you'll lose them for sure if they don't get to eat.
My 2 cents.
AT