Turn on the oven to preheat to 190 degrees. Prepare the filling. Cut the fish fillet into cubes about 2×2 cm, sprinkle with flour. Cut the shrimps into 3-4 pieces.
In a large skillet, heat the oil mixed with 1 tablespoon of butter. Pour green onions into a preheated pan and fry, stirring occasionally, for about 2 minutes.
Add chopped garlic to the skillet and cook over low heat until the onions are soft, about 5 minutes. Transfer the contents of the skillet to a large bowl.
In the same frying pan, heat the remaining vegetable oil and 2 tablespoons of butter. Put the flour-dipped fish in the pan. As soon as the fish begins to brown, immediately remove it from the pan and transfer it with a slotted spoon to a bowl of onions. Put the shrimps in the same pan and fry until pink, for about 2 minutes. Transfer the shrimp to a bowl of fish and onions.
Add rice, ginger, coriander, and lime zest to a bowl. Mix well, being careful not to break the fish pieces.
Beat the egg lightly with water. Sprinkle flour on the work surface. Layout the dough and roll it into a thin layer, cut into squares about 10×10 cm in size. Place 1 tablespoon of the filling in the center of each square, put a little butter, and lightly grease the edges with a beaten egg and fasten.
Place the items on an oiled baking sheet and brush with beaten egg. Place the baking sheet in a preheated oven and bake the pies for 12-15 minutes, until golden brown.