Combine sugar, water, ginger, lemon zest, and lemon juice together in a saucepan; bring to a boil, reduce heat to medium, and cook for 10 minutes. Cool syrup to room temperature, transfer to a container, and refrigerate until flavors blend, 8 hours to overnight.
Sift flour, baking powder, and salt together in a bowl. Rub the butter into the flour mixture with your fingertips until mixture has a cornmeal texture. Add the milk; mix until a smooth dough forms. Wrap the dough in plastic wrap and let it rest for 2 hours.
Turn the dough out onto a lightly floured work surface and roll into a 5x14-inch rectangle about 1/4-inch thick. Cut the dough into twenty eight 1/2-inch wide strips. Twist pairs of strips together and pinch the ends together. Repeat for all of the strips. Cover strips with a clean cloth and let rest for 15 minutes.
Heat about 2-inches of oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Place a wire rack over a baking sheet.
Pour some of the cold syrup into a bowl and return remaining syrup to the refrigerator.
Working in batches, fry koeksister twists in hot oil until twists swell and are golden brown, 2 to 5 minutes. Remove koeksisters from hot oil with a slotted spoon and immediately immerse in cold syrup for 10 seconds. Transfer soaked koeksisters to prepared wire rack to cool. Replenish cold syrup as necessary.
