Supposably is usually wrong; supposedly is usually the word you want. Find out which one you need.
It would be much easier if I could tell you that supposably isn't a word, but I can't. It is a word, but the problem is that supposably doesn't mean the same thing as supposedly and most people use it incorrectly.
The word you usually want is supposedly, which means roughly "assumed to be true" and almost always includes a hint of sarcasm or disbelief:
Supposedly, he canceled our date because of a family emergency.
She supposedly sent the check, but it was lost in the mail.
Supposably means "supposable," "conceivable," or "arguably." It is only a valid word in American English; the British wisely refuse to accept it.
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