I have heard people use kina or kin a. I was told that people from Cap-Haïtien or Okap uses this variant. It is the possessive pronoun and adjective. Can you make a comparison between kina(Okap's version) and pa(standard version) in all persons?

People from the North also use "kin an mwen" or "kinan'm" to indicate that a person is close, dear or special to them. I would not call it an adjective or pronoun.  I would just say that it's possessive indicator or marker until the Haitian department of education says otherwise.

They don't just use this expressive form with the word "kin", they use it with other words too.
examples:
Sa se kay an mwen.→ This house is mine
Sa se pitit an mwen.→ This child is mine
Sa se pitit a ou?.→ Is this your child?
Ayiti, se peyi an nou. → Haiti is our own.
Sa se kin an mwen.→ This is mine. This is my buddy, This is my chum

kin an mwen (pa mwen or pa'm) → mine
kin an ou (pa ou or pa'w) → yours
kin a li (pa li or pa'l) → his, hers
kin an nou (pa nou or pa'n) → ours
kin a yo (pa yo) → theirs

But, you should leave it to the kapwa to talk like that.  It's THEIR way, not ours. Sometimes, when we try to talk like them, it might appear as if we're making fun of them.

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