Place the chopped potatoes in a large pot, cover with salted water, and bring to a boil. Cook until tender, about 10 minutes; drain well.
Return the drained potatoes to the pot or a bowl and mash until smooth. Stir in the cream cheese until incorporated.
Fold the minced garlic, smoked paprika, drained tuna, and chopped parsley into the mashed potatoes until evenly combined.
Shape the mixture into thick patties of your desired size, using wet hands if needed to prevent sticking.
Set up a dredging station: beaten eggs in one shallow bowl and a mixture of panko and regular breadcrumbs in another.
Dip each patty first into the beaten eggs, then coat thoroughly with the breadcrumbs. Press the crumbs on gently to adhere.
Pour about 1/2 cup oil into a non-stick skillet to reach roughly 1/2-inch depth and heat over medium until hot but not smoking.
Fry the croquettes in batches, turning occasionally, until golden brown on all sides, about 4–6 minutes per batch. Adjust heat as needed to avoid burning.
Transfer cooked croquettes to a plate lined with paper towels to drain any excess oil. Sprinkle with extra chopped parsley if desired and serve immediately.