The French doughnut often dusted with powdered sugar and typically square is a beignet.
A beignet is a deep-fried pastry of French origin. The name covers several related preparations, including versions made with pâte à choux, yeast-leavened dough, rice flour, or other batters. Confectioners’ sugar is the most familiar topping, giving the pastry its snowy appearance.
The square or rectangular version is especially associated with Louisiana, where French colonists and Acadians helped establish the pastry in New Orleans during the 18th century. Louisiana-style beignets generally use leavened dough rather than choux pastry. They are rolled, cut into squares, fried, and served hot, often as a breakfast pastry or dessert.
That New Orleans style is why beignets are sometimes mistaken for a uniquely American treat, even though the name and broader pastry tradition are French. They also should not be confused with madeleines, brioche, or croissants: those are baked French pastries, while a beignet is defined by its fried preparation. Some beignets are round, filled, savory, or made with fruit, so “square” describes a well-known style rather than every beignet.