Thaw the fish paste if frozen and place it in a mixing bowl.
Add the beaten half egg and the Thai red curry paste to the fish paste.
Stir and knead the mixture until smooth and the curry paste is evenly incorporated.
Fold in the thinly sliced snake beans and the finely shredded kaffir lime leaves until distributed evenly.
Heat oil in a deep pot or frying pan to about 350°F (175°C) for deep-frying.
Wet your hands, scoop about a ping-pong-ball-sized portion of the fish mixture, and flatten it into a patty with your palms.
Carefully slide the patties into the hot oil and fry in batches until golden brown and cooked through, about 2–3 minutes per side depending on thickness.
Use a slotted spoon to transfer cooked fish cakes to a paper towel-lined plate to drain excess oil.
Serve the fish cakes hot, paired with Thai cucumber salad or your preferred dipping sauce.