Hey guy I own a 02 f-150 ext cab 4x4 5.4L and it's skipping and jerking baddddd no coil codes replaced egr cleaned throttle body used seafoam

On behalf the battery is jimmy rigged could be the cause for the jerk/ skip? Mainly on acceleration or up hills by does do it around constant speed and main gear changing 30-40 55 and 60-75 rpms shoot to zero then back up causing the jerk idk what would cause this mainly coils I here ppl say but I got 0 codes for that