"papa m rele m pa m"? (my father - calls me - mine)? (my father calls me his own?)

Your first translation captured it.
Papa'm rele'm pa'm.
as if to say My father would call me "my own".
My father is called my own.

The expression, here is made with "rele"

1. Lajan m rele m pa m, m gen dwa fè sa m vle avè l.
    as if to say: The money calls me, "master" or The money calls me, " mine!"
    The money is mine, I have the right to do what I want with it.

2. Machin nan rele m pa m, m gen dwa vann li si m vle.
    another way to say it in Creole.
    Machin nan rele m chèmèt chèmtrès, m gen dwa vann li si m vle.
    The car is mine, I have the right to sell it, if I please.

3.  Kay la rele m pa m.  E mwen di ou pa ka rantre. Pwen final.
     The house is mine.  And I say you can't come in.  End of story.

4.  Liv la rele m pa m.  Si m pa vle prete w li, ou pa ka fè m chanje lide m.
     The book is mine.  If I don't want to lend it to you, you can't make me.

5.  Kò m rele m pa m.  M gen dwa fè sa m vle ak li.
     My body is mine.  I can do whatever I want with it.

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