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Without knowing what the fault codes and descriptions are that are stored in the engine control module (which triggers your check engine light), I can't provide an accurate diagnosis. However, based on the provided information I will give you some insights.
Let's assume that your engine is actually misfiring. Misfires can be caused by many, many things related to an imbalance in the combustion process. On a TT, though, I am going to suspect ignition coils or a mass air flow meter. If you know on what cylinders your misfires are happening, swap coils with known good cylinders and see if the misfires move with the ignition coils. If they do, replace your ignition coils. Ignition coils also act up more once they get hot. To eliminate the mass air flow meter as a possibility, unplug it. It is located between the airbox and the flexible rubber tube that goes to the back of the engine (to the turbocharger). If you unplug, the mass air flow meter and your engine runs fine (check engine light will still be on), then replace your mass air flow meter. A mass air flow meter may also not malfunction until the car has been driven for a few miles.
Note: When checking for faults, make sure you are using an Audi compatible scan tool. Also, check with your local Audi dealership and make sure there aren't any service actions open on your car or vehicle updates available that may be covered under warranty.
I hope this helps.