It helps to mention which shell you're using if you us to help with its quoting mechanism. Looks like bash or similar.

You want bash to do

system(
    q{perl},
    q{-lane},
    q{print "John's";},
);
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The first two parts are no-brainers since they contain no characters that are special to bash. Let's focus on the third.

• You could escape every special character

  print\ \"John\'s\";
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• You could use double quotes and escape the characters that are special in double quotes.

  "print \"John's\";"
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• You can't use single quotes, at least not alone. There's no way to include single quotes in a single-quoted bash literal. What you can do is use different mechanisms for different parts of the string (as in q{print "John}.q{'}.q{s";})

  'print "John'"'"'s";'
  'print "John'\''s";'
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perl -lane 'print "John'\''s";'
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Note that the following is also acceptable to Perl:

system(
    q{perl},
    q{-lane}.q{print "John's";},
);
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That could be written as

perl '-laneprint "John'\''s";'
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perl -lane'print "John'\''s";'
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