What traditional Polish quark is used in sernik?

The traditional Polish quark used in sernik is twaróg.

Twaróg is a soft, fresh, fermented-milk curd made by separating whey from milk. It is a staple of Polish cooking and is also known as ser biały, or “white cheese.” For sernik, cooks generally use a relatively dry, finely ground version so the filling sets properly rather than becoming watery.

Sernik is a baked Polish cheesecake whose recorded tradition reaches back to the 17th century. Unlike many American cheesecakes, it is built around twaróg and relies more heavily on eggs and butter, traditionally without cream or sour cream. The resulting texture can be denser and more curd-like, with a distinct dairy tang.

The alternatives in the question are cheeses from other culinary traditions: mizithra is Greek, brocciu is associated with Corsica, and mascarpone is Italian. They may appear in other cheesecake recipes, but they are not the traditional Polish cheese named by the dish’s standard description. Twaróg is also used in pierogi fillings and other Polish dumplings.