Jquery – Uncaught TypeError: Cannot use ‘in’ operator to search for ‘324’ in

You have a JSON string, not an object. Tell jQuery that you expect a JSON response and it will parse it for you. Either use $.getJSON instead of $.get, or pass the dataType argument to $.get:

$.get(
    'index.php?r=admin/post/ajax',
    {"parentCatId":parentCatId},
    function(data){                     
        $.each(data, function(key, value){
            console.log(key + ":" + value)
        })
    },
    'json'
);