My father worries about my riding a motorcycle which case is the underlined pronoun

The pronoun in this sentence is "my" which is a possessive pronoun.

Explanation:

Possessive pronouns are the types of pronouns that make a reference to speech people indicating a relation of ownership. Possessive pronouns maintain a close relationship with personal pronouns as they indicate what belongs to persons indicated by personal pronouns.

well if you have a lion for example it will kill you and that's why you shouldn't have and exotic animal