Line an 8-inch square baking pan with parchment paper so the paper hangs over the sides of the pan.
Stir together cream cheese, mozzarella cheese, crabmeat, green onions, powdered sugar, salt, and garlic powder in a bowl until combined. Transfer to the prepared pan, spreading to an even layer. Freeze for 30 minutes.
Lift cream cheese mixture from the pan using the parchment paper. Cut the frozen block in half, then cut each half crosswise into 8 sticks (you will have sixteen 4x1-inch sticks.)
Put flour in a shallow dish. Beat eggs and water together in a second shallow dish. Put panko in a third shallow dish.
Dredge each cream cheese stick in flour; shake off excess. Dip into egg mixture, then lift up so excess egg drips back into the bowl. Press into panko to coat both sides. Place the breaded sticks on a baking sheet and freeze for 15 minutes.
Preheat the oven to 200 degrees F (95 degrees C).
Add 1 1/2 inches of oil to a medium saucepan. Heat oil to 375 degrees F (190 degrees C).
Fry 3 or 4 sticks at a time until golden brown, about 1 minute. (Keep uncooked sticks in freezer until ready to fry.)
Drain fried sticks on paper towels, then transfer to a baking sheet and keep warm in the preheated oven. Repeat to fry remaining sticks.