Step 1: Understanding Indirect Speech.
In indirect speech, the question is reported without using the question mark and converting the question into a statement. We also change the tense to past when necessary. The speaker is asking about what he could do, so the correct form is I asked my sister what I could do for her in that matter.
Step 2: Conclusion.
The correct indirect speech form is (1) I asked my sister what I could do for her in that matter.