Fatherless means without a father. When Claudius killed Hamlet's father, Hamlet became fatherless and obsessed with vengeance.
Use the adjective fatherless to describe your orphaned kitten, who has no parents and is therefore both motherless and fatherless. Usually, a fatherless person has lost his or her father to death, although you could also describe a girl raised only by her mother as a fatherless child. The root of fatherless is the similar Old English word fæderleas.