Following may help you in same, also you haven't mentioned if there are 1 or more occurrences of "" apart from shown in your sample post in a single line, so assuming you have only 1 occurrence of "" in a single line.
Could you please try following sed solution and let me know if this helps you.
sed -n 's/\(.*"\)\([^"].*\)\(".*\)/\2/p' Input_file
Output will be as follows.
-A y -L
EDIT: Sorry was busy in a deployment so couldn't give explanation for code posted in POST#2. Following is the explanation for code posted in POST#2 as follows.
awk '{match($0,/".*"/); ###### using match keyword in-built awk functionality for matching the regex into Input_file. Here patteren is match(LINE,REGEX).
A=substr($0,RSTART+2,RLENGTH-3); ###### creating a variable A whose value is equal to substring of line's starting point which is RSTART+2 and line's end point which is RLENGTH-3. NOTE: variables RSTART and RLENGTH are again awk's inbuilkt variables which will get values once a regex match is TRUE while using match keyword.
if(A){print A}} ###### Making sure here value of A is present then printing the value of variable A then.
' Input_file ###### mentioning the Input_file here for same.