Additional power draw on the accessory circuit places increased load on the alternator which in turn causes the engine to run a little harder than it otherwise would. Thus burning a little extra fuel.
They produce based on current draw, but have a maximum output, usually around 60-85a for and older car, to 120-240a at 14.4vdc for a newer car or truck. There is no permanant magnet, so the coils require power to generate power. Its quite interesting.
Further to this the 12V battery effectively acts as a big capacitor while the car is running, to smooth out the power that is available.
I found this out the hard way a couple of years ago. My 12V was dead, yet I managed to jump start the car and get it running. I thought it would be ok to drive to get a new battery, as long as I kept the engine running high enough. After a couple of km the dashboard lights started to dim, so I tried reving it as high as I could, but the battery wasn't able to buffer the power and supply the ignition system, so the engine stopped. It was rush hour and I was in the middle lane, so it wasn't a particularly fun wait for the tow truck.
In the old days of lower power alternators (or really old days of generators), and lower power engines, the revs would drop noticeably, and the note change, when you turned dip lights on, aircon or even occasionally - in smaller cars - the heated rear demister! Made it very obvious the engine was working harder.
Now that tickover and fuel injection is computer controlled or we have EVs, and there's a far heavier electrical load in all cars all the time, you never notice any more. They all take power, and decrease fuel efficiency.