2007 Ford F250 Timing

This vehicle is a 5.4liter. The engine runs badly, back firing, no power , the more fuel you give it the worse it runs. We changed spark plugs, individual coils, cam shaft sensors. The cam shaft is in time with the crank shaft. I am wondering about the timing phaser or what else could cause this. When calling the ford dealership they are not aware of the timing phaser being a problem.
It is also throwing codes of #1,3 and 6 cylinders misfiring, Misfire at start up and erratic timing.