The brief
The A3 had a rough idle, fuel economy had dropped, it had got harder to start, the engine stalled now and then, performance was down, and a check engine light was on. That spread of symptoms is a misfire. A misfire is a cylinder that isn't lighting cleanly. When that happens you lose the power that cylinder should give, the engine runs uneven so it idles rough and stalls, it burns more fuel, it cranks harder, and the computer flags it. The parts behind it are the spark plugs, which wear out, and the ignition coils that sit on top of them, which fail with age. On an engine showing all of that, both are suspect, so it needs a proper diagnostic scan rather than guessing at one part.
The diagnosis
The scan confirmed the misfire and pointed at the ignition side. The plugs came out worn past spec, well into their replacement window. With the plugs that tired and a misfire logged, and the coils being the same age and the same wear item, the call was to refresh the whole ignition side, a fresh set of plugs and a fresh set of coils, rather than chase one cylinder.
The work
New genuine Audi-spec spark plugs went in, gapped to spec, and new genuine Audi-spec ignition coils went on top of them. The harness clips were reseated, and the stored fault codes cleared. Then the engine was run to confirm it was firing cleanly with no shudder, followed by a road test to confirm the idle was steady, the stalling was gone, the starting was clean, and no misfires returned.
The outcome
Steady idle, clean starts, no stalling, fuel economy back to normal, and the check engine light out after a drive cycle. The A3 went home running cleanly. Plugs and coils are wear items that age together, so doing the full set in one go means even, reliable ignition rather than another misfire a few thousand kilometres down the road.