I do not think this question makes a lot of sense as a system-agnostic question, and I am answering on the basis of systems with which I am most familiar. I strongly suspect that there are other systems where what I say would be flat-out and explicitly wrong. However, there have been claims that 95% of systems handle these things the same way, which, if true, may make this answer useful.
A successful check should never have the character positive of something that is false. A mediocre check (or a very high difficulty) may result in uncertainty, but the character should be aware that he is uncertain unless he rolls badly. Even then, rolling badly is intended to mean more “you don’t know” than it is “there’s no such thing as a jabberwock; everyone knows that!”
On the other hand, being sure of oneself, when one is in fact wrong, is pretty common, in stories and in real life. As a result, it may be an appropriate thing to have in a game. Again, it is much more common when the person in question knows a little bit – the Dunning-Kruger effect, for example – so this should usually be the realm of low rolls. And in many games, it is inappropriate to punish characters for doing well, but not well enough, even though this is a common theme in reality (“a little knowledge is dangerous”). Being misled ought to be a function of significant failure.
If you have a secret the players are not meant to know, that’s a plot point and really shouldn’t be a matter of rolling. Rolling dice when the answer is predetermined just slows down play.
Regardless of how you set it up, however, it is important to explain it to your players ahead of time, ideally before the game starts. Obviously, it is not a thing to bring up just as you’re deceiving them, since that would be a dead give-away, but a lot of players will assume that by the nature of the game and its rules, Knowledge checks are infallible. You need to explain that what they are told upon rolling Knowledge is what they remember, believe to be true, think they know, etc.
If certainty-in-the-inaccurate is to occur only on very poor rolls (which I recommend), you should also probably be rolling the dice in secret for Knowledge checks. In which case you also have to describe how certain the character is: “you’re absolutely certain” for high rolls, “you’re pretty sure it went like this” or “common knowledge says that this is so” for medium rolls, “you just don’t know” for low rolls, and “you’re absolutely certain (and you’re wrong)” for the lowest rolls, or perhaps only on the lowest roll.