2007 Ford F-250 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.