The people who claim that having fast in the day of mid-Sha'ban is valuable depend on their this claim for the reason that they think the night of that day is special. They have no any other reason. Since that questionthat question explains that their this assumption was wrong, and that day didn't have any specialty at all, the hadiths about his matter were weak, then we understand that having fast in that day has no extra benefit. If you have fast that day, your fast becomes a normal fast; it wouldn't give you any bonus sawabs.
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