Preheat the oven to 350 degrees F.
For the marinade: Combine the balsamic vinegar, lemon juice, thyme and garlic in a small mixing bowl. Season with salt and pepper. Set aside until ready for use.
For the peppers: Heat the oil in a medium saute pan over medium-high heat. Once hot, add the onions and saute until translucent, about 3 minutes. Add the peppers and continue to cook to just get a little color on the vegetables, about 2 minutes. Season with salt and pepper and saute until just fragrant, about 30 seconds. Remove from the heat and reserve.
For the catfish: Take four 12- by 12-inch sheets of parchment paper and place on a clean work surface. Working with one packet at a time, begin by folding a piece of parchment paper in half to make a crease down the middle. Open it back up and spoon about 1/3 cup of sauteed peppers and onions onto the middle of the parchment paper. Place a fillet of fish on top. Drizzle 2 tablespoons of the marinade over the top and sprinkle with salt, pepper and a pinch of paprika for color. Fold the parchment back over the fish to enclose. Working from one corner and around the fish to the other corner, make small folds that overlap one another so the packet gets tightly sealed. Continue to fold crease over crease until the packet is sealed. Tuck the last fold under the packet to hold in place.
Repeat with all four packets, and then place on a sheet tray and into the oven. Bake until the packets puff up completely, 10 to 12 minutes.
To serve: Open the parchment packet tops with scissors and garnish with parsley, scallions and lemon wheels.