Yes, it is correct to say "father's nationality" when referring to the country of nationality of someone's father. The possessive form "father's" indicates that the nationality belongs to the father.
Batista comes from the Philippines(his father's nationality) and from Greece(his mother's nationality).
I asked my Mother and Father what my nationality is.
Demi's father is Hispanic.
Kevin Youkilis is American, but his father is of Romanian ancestry.
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Dian fossey the zoologist her nationality was American, her father George fossey was Irish
Italian
Her nationality is American. Ethnically she is Chinese (Father) and Black (Mother).
Vanessa Hutchin's nationality is Filipino, Chinese (from her mother); Irish and American Indian (from her father).
His nationality is Canadian His ethnicity is Half White (mother) and half black (father).
British Mother & Moroccan Father