Prep the Cheeks: Use paper towels to pat the bluefish cheeks completely dry. (This is a critical step; any moisture will steam the fish rather than sear it.) Lightly season the dry cheeks with a pinch of salt.
Prepare the Dredge: In a shallow dish or a sealable plastic bag, combine the all-purpose flour, garlic powder, 1 tsp salt, and black pepper. Whisk or shake until well combined.
Dredge: Working in small batches, coat each cheek lightly in the flour mixture. Shake off any excess flour—you want a thin, translucent veil, not a heavy batter.
Heat the Pan: Place a cast-iron or heavy-bottomed skillet over medium-high heat. Add the olive oil and wait until it is shimmering and you're just starting to see wisps of smoke.
The Sear: Carefully place the cheeks in the skillet in a single layer. Do not overcrowd the pan; work in two batches if necessary to maintain the oil temperature.
Cook: Sear the first side for 2–3 minutes until the edges are noticeably golden and crisp. Carefully flip the medallions using a thin spatula.
The Finish: Cook the second side for another 1–2 minutes until the meat is opaque and flakes easily with a fork. Optional: Add the tablespoon of butter to the pan during this final minute, basting the cheeks as it melts for added richness.
Serve: Remove the cheeks from the skillet and drain briefly on a paper towel-lined plate. Serve immediately, while hot, with fresh lemon wedges to cut through the oiliness.