Make beer batter: Combine flour, cornstarch, baking powder, and salt in a large bowl. Blend beer and egg in a separate bowl, then quickly stir into flour mixture until combined with a few lumps remaining.

Make white sauce: Mix together yogurt and mayonnaise in a medium bowl. Gradually stir in fresh lime juice until consistency is slightly runny. Season with jalapeño, capers, cayenne, oregano, cumin, and dill.

Start fish tacos: Heat oil in a deep-fryer to 375 degrees F (190 degrees C).

Season fish with kosher salt and pepper. Dust fish pieces lightly with flour. Set aside.

Dip floured fish pieces into beer batter. Set aside.

Fry in hot oil until crisp and golden brown. Drain on paper towels. Lightly fry tortillas in hot oil until just crisped, but not too crisp. Drain on paper towels.

Dice onion and slice lime. Chop cilantro and cabbage.

Place fried fish in tortillas; top with shredded cabbage, cilantro, onion, lime, cojita cheese, and white sauce.