Contractions use apostrophes: can't, shouldn't, won't. The idea is that the apostrophe represents missing letters: can't becomes cannot, shouldn't becomes should not, won't waves its magic wand to become will not (because willn't would just be silly ... but I still adore the underused amn't).
This extends to the representation of mispronunciations and lazy speech: Oh, I s'pose so; "Goin' Down to South Park"; "Mary, Mary, why you buggin'?" Here, again, the apostrophe represents elided letters or syllables.
But there is a class of similar terms representing the common pronunciation of phrases ending in to. Most people I know -- myself included -- don't fully enunciate want to or going to, for example. If I'm writing dialect, I will represent that as an alternate spelling: I don't wanna and I'm not gonna.
But I know people (hi!) who would instead write that as I don't wanna' and I'm not gonna'.
I don't know that there's a "right" or "wrong" when it comes to representing speech. But as I see it, in this case, there aren't elided letters to represent. Those letters have instead been replaced, so the apostrophe doesn't belong.
Yet this usage doesn't belong only to one person; I've seen it in several different contexts, though still only in a minority of cases. It seems to me that it might be a New England thing, but that's just an impression I've picked up.
So: Does anybody 'round here know more on this subject? Are these types of apostrophe usage covered in schools or usage manuals? Do you know of any regional influence on the subject? Bonus question: is there a formal term for the conversion of want to to wanna(')? I'm interested in citations, opinions, related ramblings, or any other contributions, so feel free to chime in!