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Nationality is usually a matter of domestic law, so the law of the father's home country would apply to assess whether or not the child is a national of that country by virtue of the father being a national of that country.
The father should try and find out whether the child is eligible for nationality of this particular EU country so that the child can get entry to that country.
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"Nationality is defined according to the national laws of that State. "
See under Definition of EU Citizenship: https://www.europarl.europa.eu/factsheets/en/sheet/145/obywatele-unii-europejskiej-i-ich-prawa
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