Preparation
1. Drain salsa in mesh strainer over bowl. Reserve strained salsa and 1/3 cup juice separately. Meanwhile, adjust oven rack to middle position and heat oven to 450 degrees. Brush rimmed baking sheet with 2 tablespoons oil.
2. Combine chicken, taco seasoning, jalapeños, cheese, and salsa juice in bowl. Spread 1 cup filling over half of each tortilla, leaving 1/2-inch border around edge. Brush plain half of tortillas with oil, fold over filling, and press down firmly. Transfer to prepared baking sheet and brush tops of each tortilla with 1/2 teaspoon oil.
3. Bake until tops of quesadillas begin to brown, about 10 minutes. Flip quesadillas over, press with spatula, and bake until crisp and golden brown on second side, about 10 minutes. Cool quesadillas on wire rack for 10 minutes before slicing. Cut each quesadillas into 4 wedges and top with reserved salsa. Serve with sour cream.