a friend of mine, etc

We cannot usually put a possessive between another determiner and a noun. We can say my friend, Anna’s friend, a friend or that friend, but not a my friend or that Anna’s friend. Instead, we use a structure with of + possessive.

Grammar

determiner + noun + of + possessive

• That policeman is a friend of mine.
• How’s that brother of yours?
• He’s a cousin of the Queen’s.
• She’s a friend of my father’s.
• Have you heard this new idea of the boss’s?
• My work is no business of yours.
• I met another boyfriend of Lucy’s yesterday.

The structure has a variant in which a noun does not have possessive ’s: this is sometimes used when talking about relationships.

• He’s a cousin of the Queen.
• She’s a friend of my father.

The word own is used in a similar structure (see here).

• I wish I had a room of my own.