Place the chicken breast and potato halves in a pot and cover with water. Bring to a boil, then simmer until the chicken is cooked through (165°F) and the potato is fork tender, about 20 to 25 minutes. Drain and set aside.
Transfer the chicken to the bowl of a stand mixer fitted with the paddle attachment. Mix on low until finely shredded. Add the potato and mix until mashed.
Add the eggs, garlic, parsley, breadcrumbs, turmeric, paprika, salt, and pepper. Mix until everything is fully combined.
Shape a small patty and sear it. Taste it and check that it holds together, then adjust the seasoning if needed.
Shape the rest of the mixture into about 20 patties, 2 to 3 inches wide.
Heat the oil in a nonstick pan over medium-high heat. Sear the patties in batches for about 5 minutes on each side, until golden and heated through.