PowerShell, 132 Bytes
$a='$a=;for(){$a.substring(0,3)+[char]39+$a+[char]39+$a.substring(3)}';for(){$a.substring(0,3)+[char]39+$a+[char]39+$a.substring(3)}
Based off of the Rosetta Quine (Same as @AdmBorkBork) although doesn't use formatting for string replacement... maybe switching to a for loop and using formatting would be best?
I'm sure if AdmBorkBork came back they would beat this by a lot :P