There are suppositions that supposably is not a word and that what one means to say is supposedly. The thing is, supposably is a word, but because it’s often incorrectly used in lieu of supposedly, it sounds wrong, which explains why so many suppose it is.
Let’s look at these two adverbs along with a couple of other related words.
Supposedly suggests a permitted behavior or action:
Supposedly, it’s OK to smoke in here.
In contrast, supposably implies something that’s imagined:
He was going to ask her to marry him, supposably.
Supposed, not suppose, is often used in conjunction with the preposition to. In this context, supposed is an adjective that means “to be regarded as true or intended,” even if only skeptically so. For example: