Yes. Nationality means that your ancestors and/or you come from a particular country. Jamaica is a country, so it fits the definition.
Anyone from Jamaica would be considered Jamaican.
Jamaican
She is Jamaican
C Everard Palmer is a Jamaican author.
jamaican
Jamaican
She has Jamaican roots.
Jamaican-American
50% jamaican lair he's not jamaican i know him he's haitian
Ewing is Jamaican-American.
Japanese, Jamaican, and Black
He is Jamaican but migrated to Canada in 1976