Prepare the stock: Heat olive oil in a large pot over medium-low heat. Add garlic, celery, carrot, and onion and cook, stirring, until golden brown, about 10 minutes. Add fish bones and head and enough water to cover. Bring to a simmer; reduce heat to a gentle simmer and let cook for 25 minutes, skimming the surface as necessary. Strain through a fine mesh strainer; discard solids and set aside.
Prepare the suquet: Place a grater over a bowl and rub the cut surface of the tomatoes over the grater until all the flesh is grated; discard skins. In a deep pot, heat olive oil over medium heat. Add potatoes and cook, stirring, for two minutes. Stir in grated tomato and sugar, if using; continue cooking 2 minutes more. Add saffron and pimenton and cook for one minute.
Add enough stock to just cover the potatoes. Increase heat to medium-high and bring to a boil, then reduce heat to low and simmer until potatoes are cooked through, about 10 minutes.
Prepare the picada: Using a mortar and pestle, mash garlic and salt together until a thick paste is formed. Add parsley and one piece of potato from the stew; mix until well combined. Set aside.
Season fish fillets with salt and cut each in half so you have four equal pieces; add to pot along with clams. Cook until clams begin to open, 4 to 5 minutes. Stir in picada and season with salt. Serve immediately with allioli, if desired.