Aschilebi 1086 (Domesday Book). "Farmstead or village of a man called Áskell". Old Scandinavian personal name + "by".
"A Dictionary of English Place-Names", Oxford University Press
Asselby is a village on the dead-end road between Barmby-on-the-Marsh and Knedlington. It gives its name to Asselby Island, the nearby large woodland area where the Ouse meets the Aire.