Dutch settlers brought Doughnuts to New York
Dutch settlers brought olykoek ("oil(y) cake") to New York (or New Amsterdam). These doughnuts closely resembled later ones but did not yet have their current ring shape. The name oly koeks was almost certainly related to the oliekoek: a Dutch delicacy of "sweetened cake fried in fat."
The first cookbook, using the near conventional "dough nuts" spelling, was possibly the 1803, New York, edition, of "The Frugal Housewife: or, Complete Woman Cook", which included dough nuts in an appendix of American recipes.
One of the earliest mentions of "doughnut" was in Washington Irving's 1809 book A History of New York, from the Beginning of the World to the End of the Dutch Dynasty.
'Sometimes the table was graced with immense apple-pies, or saucers full of preserved peaches and pears; but it was always sure to boast of an enormous dish of balls of sweetened dough, fried in hog’s fat, and called dough-nuts, or oly koeks: a delicious kind of cake, at present scarce known in this city, excepting in genuine Dutch families.'