Preheat oven to 350°F. In a bowl, stir together flour, baking powder, baking soda and salt. Add scallions and Cheddar; mix well. Fold in butter and beer, mix until just combined.
Turn dough out onto lightly floured work surface; pat down to 1-inch disk. Use a 3-inch round cutter to cut biscuits. Gather scraps, pat down again and cut remaining biscuits. Place biscuits on ungreased baking sheet.
Brush biscuits with milk; sprinkle with paprika. Bake for 25 minutes, until golden. Serve warm.