Long debate about whether it's "supposedly" or "supposably"
It's both, and they have different meanings!
"Supposedly" means "according to what is generally assumed or believed (often used to indicate that the speaker doubts the truth of the statement)."
"Supposably" means "As may be imagined or conceived. It suggests a possibility rather than a certainty. Best used when you want to say something is within the realm of possibility or could be imagined. It is often used with modal verbs like could, may, or might."
So, in easier words, "Supposedly" means there are rumors you have doubts about, like "She was supposedly at the party last night." Meaning you have doubts about whether she was.
"Supposably" means there are rumors you DON'T have doubts about, like above with "possibility" rather than certainty, like "Supposably, she was at the party last night." meaning you likely believe that she was.