Learn English – My or Mine usage

The correct phrasing is my question is.

As you rightly note, my is a possessive adjective and mine is a possessive pronoun. So, this means you use my where you already have a noun (such as question) and want to indicate ownership. Like with all pronouns, you use mine in place of another noun when it's understood what's being discussed.

Mine question is is ungrammatical, because it incorrectly uses two nouns (mine and question) as the subject of a sentence. You use either a noun or a pronoun, never both at the same time. Use a noun (my question) if the topic is just being introduced, or a pronoun (mine) if the reader or listener will already know you are talking about (they will know you are talking about your question).

The following are correct:

• My question is [something] uses my to indicate whose question is being described.
• That question is mine uses mine to refer back to the subject (that question) and add information describing whose it is.
• Mine is [something] describes some object of yours (e.g. your question) which was previously named and is currently the topic of conversation.

It is customary in English, though it may not make sense to you, to use the so-called "double possessive":

He is a friend of mine.

He is a friend of my father's.

Even in cases like

That is a favorite book of mine.