I dont really know how steel is manufactured IRL, so I had to do a little bit of research there to figure some stuff out. Some of my information could be wrong.
Resource hunting and logistics
I know that steel is just iron and carbon, so you need to obtain those 2 things. You have iron rich asteroids, and asteroids with carbon. I dont know if theyre close by where our station needs to be but if the station's asteroid is big enough and the asteroids small enough you could push the resource asteroids to get into orbit around your station's asteroid. If you cant get an asteroid into orbit around your station youll just have to get that resource asteroid in orbit around whatever your stations asteroid is orbiting, as close as you can to the station. That way you can use those resources more easily than if you had to mine at that asteroid and then go ALL the way back to the station. Just bring the mine to you. A little bit of delta V and a lot of time can move stuff around just fine.
You also want icy asteroids. You need water, or at least, oxygen, which you could get from water, from ice. Get Ice.
Utility of oxygen
You want oxygen because simply melting iron ore and adding carbon wont work. Your steel will be impure, and i want pure steel in my space ships. To prevent this, (pure) oxygen is blown through the molten iron which will react with impurities to make the molten iron more pure. This is a massive simplification of steel production, Here is more on the Basic oxygen process that im going off of.
Heat and power management
I originally had 2 paragraphs typed out and then realized a diagram would be easier. So I made one. Ill still provide some additional notes on some things where needed. Power and heat generation are tied together heavily, and thats why the diagram only shows heat, because really, theyre both energy, and in this case, energy that doesnt really leave the system easily, so we should try to redirect it elsewhere.
[Heat goes to water?] At extreme temperatures, water splits into oxygen and hydrogen (thermolysis, you could use electrolysis if energy is no problem). We need oxygen, a lot of it.
[carbon/hydrocarbon filtering for combustion?] Polycyclic aromatic hydrocarbons, which are... maybe existing abundantly or otherwise in space? According to some space nerds at MIT they could make up a good portion of the carbon that exists in space. Those PAHs, specifically pay attention to that hydrocarbon part. A combustion reaction is just a hydrocarbon and oxygen, which turns into CO2, water, and heat. More heat to vent, but also more heat to use for melting ice into h2 and o2, more water to be melted, and co2 which can be split back into carbon and oxygen using little power using these nanomaterials that we cant make much of yet but can make samples of.
Sure, we dont technically need the combustion part of this reaction, but it will help us liberate more carbon and heat from the system than we would without it. We get more carbon, and we get more heat to melt ice with, at the cost of some of our oxygen, which comes from ice. Its worth if you cant get enough carbon to make your desired amount of steel and you have some extra ice laying around. If youre short on ice, maybe want to hold off on it. Combustion isnt necessarily for generating energy, its for liberating more carbon, and trying to recycle as much as possbile.
This is a lot
Even assuming 100% efficiency, this is still going to have a lot of losses in the system, and require a lot of energy. Were definitely going to need to bring in a lot of asteroids, and we should probably invest in some solid power generation. And do something with that hydrogen... but, it is theoretically doable. You dont have to ship steel to space anymore, yippee!
Some questions still remain, like the hydrocarbon filtering, is the extra carbon we can liberate from the process worth the cost in splitting up and filtering carbon from hydrocarbon? Is combustion as a whole even worth it here, or should it just use a completely electricity-based heating system and skip the combustion? What power source (solar is a bad idea if you're far from the sun) do we use and how do we make it work here? These questions will remain unanswered for now, this is mostly an idea for how one could try it.