"Hello, this is my younger brother."
Translation:Здравствуйте, это мой младший брат.
The genitive case is for people or objects that own other things, not things that are owned.
Possessive pronouns don't change the case of the things they own, rather the possessive pronoun changes depending on the case of the noun being owned. So, if the noun was genitive case ("младшего брата"), you would use "Моего".