J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

##how

 single quote 
 quoted program adjustment
 | / 
 vvvvvvvvvvvvvvvv _____/___ 
(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''
^^^^^^^^ ^^^^^^^^^^
 \ /
 regular program

• Everything above a ^ is part of the "regular program".
• The rest is "the program quoted", but with one exception:
  • The quoted program doesn't include the program's single quote characters '
• 2*1#.=&'...' - Two times 2* the sum of 1#. the total number of times the input char matches a char in "the quoted program". One for the actual program char, one for its quoted twin.
• +6*=&'''' - Plus six times +6* the 1/0-indicator of whether the input char is equal to a single quote =&''''. This is the hardcoded knowledge that there are 6 single quotes in the program.

J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

how

 single quote 
 quoted program adjustment
 | / 
 vvvvvvvvvvvvvvvv _____/___ 
(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''
^^^^^^^^ ^^^^^^^^^^
 \ /
 regular program

• Everything above a ^ is part of the "regular program".
• The rest is "the program quoted", but with one exception:
  • The quoted program doesn't include the program's single quote characters '
• 2*1#.=&'...' - Two times 2* the sum of 1#. the total number of times the input char matches a char in "the quoted program". One for the actual program char, one for its quoted twin.
• +6*=&'''' - Plus six times +6* the 1/0-indicator of whether the input char is equal to a single quote =&''''. This is the hardcoded knowledge that there are 6 single quotes in the program.

J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

##how

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''
^^^^^^^^ ^^^^^^^^^^

• Everything above a ^ is part of the "regular program".
• The rest is "the program quoted", but with one exception:
  • The quoted program doesn't include the program's single quote characters '
• 2*1#.=&'...' - Two times 2* the sum of 1#. the total number of times the input char matches a char in "the quoted program". One for the actual program char, one for its quoted twin.
• +6*=&'''' - Plus six times +6* the 1/0-indicator of whether the input char is equal to a single quote =&''''. This is the hardcoded knowledge that there are 6 single quotes in the program.

J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

##how

 single quote 
 quoted program adjustment
 | / 
 vvvvvvvvvvvvvvvv _____/___ 
(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''
^^^^^^^^ ^^^^^^^^^^
 \ /
 regular program

• Everything above a ^ is part of the "regular program".
• The rest is "the program quoted", but with one exception:
  • The quoted program doesn't include the program's single quote characters '
• 2*1#.=&'...' - Two times 2* the sum of 1#. the total number of times the input char matches a char in "the quoted program". One for the actual program char, one for its quoted twin.
• +6*=&'''' - Plus six times +6* the 1/0-indicator of whether the input char is equal to a single quote =&''''. This is the hardcoded knowledge that there are 6 single quotes in the program.

J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

J, 34 bytes

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''

Try it online!

##how

(2*1#.=&'(2*1#.=&)+6*=&')+6*=&''''
^^^^^^^^ ^^^^^^^^^^

• Everything above a ^ is part of the "regular program".
• The rest is "the program quoted", but with one exception:
  • The quoted program doesn't include the program's single quote characters '
• 2*1#.=&'...' - Two times 2* the sum of 1#. the total number of times the input char matches a char in "the quoted program". One for the actual program char, one for its quoted twin.
• +6*=&'''' - Plus six times +6* the 1/0-indicator of whether the input char is equal to a single quote =&''''. This is the hardcoded knowledge that there are 6 single quotes in the program.