Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook for 5 minutes until it softens.
Stir in the minced garlic and smoked paprika. Cook for 1 minute until fragrant.
Add the diced potatoes, fish stock, saffron threads, salt, and black pepper. Bring the mixture to a simmer.
Cook uncovered for 15 minutes, stirring occasionally, until the potatoes are almost tender.
Gently add the cod pieces to the pot. Simmer for 6 to 8 minutes until the fish turns opaque and flakes easily.
Remove the pot from the heat. Stir in the chopped parsley.
Ladle the stew into bowls and serve with lemon wedges on the side.