What is correct use of 's
Solution 1:
Both could be correct depending on the scenario.
Scenario 1: Your birthday. You got a car from your father, and a laptop from your mother. You could say- this is my father's gift, and that's my mother's gift. Though, a better way to say this would be- this is the gift from my father, and that's from my mother.
Scenario 2: Your father's birthday. You bought a cake and a gift. You could say- this is my father's cake, and that's my father's gift. Though, a better way to say this would be- this is the cake for my father, and that's the gift for him.