Mostly This problem came in front when You need to use dynamic Query in which you can not use String with single quote so We have to replace ' in to \' 
There are two  Approach as follows :
If your String is InputString = "sj'ase'aa'"
First Approach
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Use String Method
string.escapeSingleQuotes(InputString);
output would be sj\'ase\'aa\'
Second Approach:
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if(InputString.contains('\'')){
                       InputString= InputString.replaceAll('\'', '\\\\\'');
}
But Second Approach is limited up to only single quote but when you use back slash you can not use this approach.
so go to first one.
 
