1. In a large bowl, combine chicken, paprika, garlic, and green onions, and season with salt and pepper. Divide mixture into 4 patties. 
2. In a large skillet over medium heat, heat oil. Add burger patties and cook, flipping once, until golden and a thermometer inserted into the center registers 165°, 8 to 10 minutes. Top with cheddar, cover, and cook until just melted, 2 minutes. Remove from heat and transfer patties to a plate.