I want to retrieve data from database and show in Checkbox using JSON.

//use this code this will help you to post the data and get the data is call back function, your action method should return the you databse value.

$.ajax({
            type: "POST",
            url: "/contrller/Actionmethod",
            dataType: "json",
            data: { value: seectedvalue }, //oyur chechbox value
            success: function (data) {
                //assign your return data where you wanto here
                });
            },
            error: function (ex) {
                alert('Failed to retrieve values.' + ex);
            },
 });