The normal way for showing possession is to use the “ezafe” (the short vowel “e” that is rarely written but is always pronounced).
رئیسِ شرکت
خانهی فاطمه
The company’s boss
Fatemeh’s house
Possession can be shown using both free and enclitic personal pronouns:
دستِ من کثیف است. / دستم کثیف است.
My hand is dirty.
To make a structure similar to the English possessive pronouns (mine, yours, hers, ours, etc), in Persian, the word “مال” is used before the free personal pronouns. The word “مال” originally means “belongings, property, etc”. This structure is usually not used in formal language.