It means that a man who is the biological father of a child admits it is his child. He acknowledges paternity or fatherhood.
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Claims of parentship
Maternal means originating from your mother's side of the family (ex. my maternal grandmother). paternal means originating from your father's side of the family (ex. my paternal grandfather)
I read somewhere that "Pickford" was Mary's paternal grandmother's name.
younger female cousin (sharing paternal grandfather)
It means "the fathers of my father are my grandparents."
Your maternal grandmother is the mother of your mother. Similarly your paternal grandmother is the mother of your father, paternal grandfather is father of your father and maternal grandfather is father of your mother.
The noun form for the adjective paternal is paternity.
A paternal niece is a niece on the fathers side. For example:my dad's sisters's daughter is my paternal niece
"Paternal" means "on your father's side". Your paternal great-grandfather would be one of your father's grandfathers.
The grandparents on the father's side of the family
acknowledgment: a statement acknowledging something or someone; "she must have seen him but she gave no sign of acknowledgment"; "the preface contained an acknowledgment of those who had helped her"