I have a 2003 325i BMW M56. Recently, I gave it a full complete tune-up from the Bosch ignition coils, the Siemens fuel injectors, the NGK iridium spark plugs, new air filter and a new valve cover gasket.

It did not backfire for a few days and the engine codes were off but then it started back backfiring under the hood from coil 1 and 4 with lean codes. It will back fire seconds under the hood at a "cold start" and then completely stops after the engine warms up and it doesn't come back anymore unless it has completely cooled back down.

Im under assumption that it could be a possible airleak or something similar but i dont know how to track nor test for it or to even stop it as it is embarrassing any help!?!

I would only use factory oem coil on plug assemblies if you didn't use that. But as for air leaks, try this video https://www.youtube.com/watch?v=NWCKvU2FmDc