Suppose you have a sentence which concludes with the eye dialect somethin' for the word something. Where does the period go? Which is correct?
This is really somethin'.
This is really somethin.'
It seems to me that the apostrophe is part of the word, and hence attaches to it as opposed to the sentence. Thus, I'd put the period after the apostrophe. The second construction looks like an error, with mismatched quotes.