The possessive forms my, your, our, his, her, their and its are determiners. They are used at the beginning of noun phrases. These words are sometimes called possessive adjectives.

Have you seen my new car?
Is that her boyfriend?
Where is your daughter?
What happened to his father?

One’s is used in the same way.

One should not lose one’s temper.

Note the spelling of the possessive its. There is no apostrophe. The form with apostrophe (it’s) is a contraction. It means it is or it has.

Note that the possessives cannot be used with articles or demonstratives.

She has broken her arm. (NOT She has broken the her arm.)
I have found your keys. (NOT I have found the your keys.)

If we have to use an article or a demonstrative with a possessive word we use a structure with of.

She is a cousin of mine.

Mine, yours, theirs etc

The words mine, yours, theirs, ours, his and hers are pronouns. They are used without prepositions.

That coat is mine.
Which car is yours?

We do not use articles with mine etc.

Can I borrow your pen? I can’t find mine. (NOT I can’t find mine pen.)