Yes a skullcap, called a zucchetto in Roman Catholic tradition,
is worn by Roman Catholic clergy in some cases. It arose during the
time when a tonsure was worn by all clergy as a way to keep the
head warm. As a rule, a purple zucchetto is worn by Arch/Bishops,
red by Cardinals, and white by the Pope; brown or black zucchetto's
are sometimes worn by Franciscan, Benedictine, and Trappist
monks.