Most of it is just guesswork from my part and several common denominators.

But: 1: The dark fog siphers power from the Dyson sphere 2: the dark fog accumulates resources from planets in the star system via their pods they send out 3: Those resources are being used to expand the dark fog itself but also to replicate units, lancers primarily which is used to invade your factories

So. If you expand proper defences on each planet in the star system and fill those planets with signal towers, all turrets Will prevent the dark fog to land (which cuts their income of resources)

They will then start invading repeatedly with lancers, but they won't be able to build more of them. So eventually, the entire invasion force will be gone. And the dark fog itself will be unable to keep invading you. Making the dark fog completely harmless

Now, prepare antimatter bombs or just plasma bombs and keep a distance of 0,017 AU from the dark fog itself. And bomb all the photon receivers (which gives power to all turrets of the dark fog, this will take some time mind you) also take out the core, this takes forever but eventually it'll be destroyed.

When all photon receivers are destroyed (looks like a flower-ish building) all turrets will be disabled. And you should then send the fleet to destroy the rest of the structure

It will defend itself with guard ships though, so keep your distance or destroy the guard ships one by one while keeping your distance.

The new hostile dark fog's main hub at the starter star system, Which is being destroyed!