Place Aleppo pepper in large bowl and mix in 1 tablespoon warm water. Let stand until thick paste forms, about 5 minutes.
Add yogurt, olive oil, red wine vinegar, tomato paste, 2 teaspoons coarse salt, 2 teaspoon black pepper to spice mixture in bowl, and garlic; whisk to blend.
Stir in garlic and lemon slices, then chicken. Cover and chill at least 1 hour or up to one day before cooking. Keep chilled.
Prepare barbecue (medium-high heat).
Thread chicken pieces on metal skewers, dividing equally.
Discard marinade in bowl.
Sprinkle each skewer with salt, pepper, and additional Aleppo pepper.
Brush grill rack with oil.
Grill chicken until golden brown and cooked through, turning skewers occasionally, 10 to 12 minutes total.
Transfer skewers to platter.
Surround with lemon wedges and serve.