Which one sounds better to you?
I'm sorry to have alarmed you with my previous email.
or
I'm sorry for alarming you with my previous email.
Thank you.
The second one will do since you are currently having conversation although the first one will also work if the person you are talking with has been alarmed by email before.
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The second one will do since you are currently having conversation although the first one will also work if the person you are talking with has been alarmed by email before.