In BrE, your nationality refers to the passport you hold. If you hold only a Japanese passport, then for official purposes, you're Japanese. If you only hold a Korean passport, then for official purposes, you're Korean. If you hold both passports, you are a "dual national" (Japanese and Korean).
If you're referring to your race or ethnicity, then you're half-Japanese, half-Korean. However, you can use "of Japanese and Korean descent" to refer to your mixture of ancestors.
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