As in all communication, the apology is in the hands of the receiver. You may be very sincere, but it is up to the receiver to determine if the apology makes its mark on them.
If your spouse is still upset after you apologize, you might ask: “I know that I hurt you. I can see it in the way that you respond to me. I am sorry. Please tell me what hurts you the most about what I said/did?”
They will likely respond in a way that gives you a clue to what they would like to hear in an apology. Apologize in the way that is most meaningful to them.