This is the 3220th most frequent Turkish word.
gazetesinin
"Gazetesinin" means "his/her/its newspaper" or "the newspaper of his/her/its" in English.
In this sentence, 'gazetesinin' is a possessive form derived from 'gazete' (newspaper) with an added possessive suffix '-si' referring to it being 'his newspaper'.
Ali gazetesinin üzerine bir şey döktü ve yazılar okunmaz hale geldi.
Ali spilled something on his newspaper, and the writings became unreadable.
Here, 'gazetesinin' carries the meaning of 'her newspaper', indicating ownership by the woman mentioned in the sentence.
Kadın gazetesinin her köşesini dikkatle inceleyerek okuyordu.
The woman was carefully examining and reading every corner of her newspaper.
In this sentence, 'gazetesinin' signifies 'his newspaper', showing the association of the newspaper to 'my friend'.