Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan with cooking spray or line it with parchment paper.
In a mixing bowl, combine the flour, baking powder, baking soda, salt, garlic powder, and black pepper. Mix well.
In another bowl, whisk together the eggs, buttermilk, and melted butter until well blended.
Add the shredded turkey, chopped onion, chopped bell pepper, and shredded cheese to the wet mixture. Stir until evenly combined.
Gradually fold the dry ingredients into the wet mixture until just combined. Be careful not to overmix.
Pour the batter into the prepared loaf pan, spreading it evenly.
Bake in the preheated oven for 40-50 minutes, or until a toothpick inserted in the center comes out clean and the top is golden brown.
Allow the turkey cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.