Inverse-quotes-quine
Python 2, 20 bytes

print&quot;;print'print'&quot;

-7 bytes thanks to tsh
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Old answer:
Python 2, 27 bytes

'';print&quot;;print 2*&quot;'';print

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Train of thought behind this answer:
Begin with a simple print, because we need to print something.
print&quot;a&quot;

We also need to print something in the inverted case, ie. have a print inside quotes.
print&quot;print&quot;

The non-inverted case is pretty good at this point. Let's focus on the inverted case. We now start with the string print, which can't be followed immediately by a print statement. Let's fix this with a semicolon.
print&quot;;print&quot;

Good stuff. Except, the inverted code doesn't actually print anything. We'll need to print the print at the start, because it ends up in quotes, but also print whatever comes after the second quote, because it ends up in quotes too. The obvious way around this is to append print and multiply the last string by 2.
print&quot;;print 2*&quot;print

Now the inverted code works fine, though we have to be wary of the fact that the section before the first quote and the section after the second quote need to be kept the same throughout future changes. As for the non-inverted code, it throws a syntax error - once again, we need to introduce a semicolon to separate expressions.
;print&quot;;print 2*&quot;;print

Python doesn't really like the look of that lone semicolon, so we must satisfy the snake's hunger with two of the same no-op expression, inserted before the first semicolon and the last semicolon. Most expressions will work fine in the first case, but in the second case it must follow print&quot;;print 2*&quot; in the non-inverted code without breaking anything. We can use '', which simply gets concatenated with the prior string.
'';print&quot;;print 2*&quot;'';print