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$("input[type='checkbox']:checked")

例

<div class="days">
  <label><input type="checkbox" data-dayOfWeek="0">日</label>
  <label><input type="checkbox" data-dayOfWeek="1">月</label>
  <label><input type="checkbox" data-dayOfWeek="2">火</label>
  <label><input type="checkbox" data-dayOfWeek="3">水</label>
  <label><input type="checkbox" data-dayOfWeek="4">木</label>
  <label><input type="checkbox" data-dayOfWeek="5">金</label>
  <label><input type="checkbox" data-dayOfWeek="6">土</label>
</div>
<script>
function getCheckedDay() {
  var days = [];
  $(".days input[type='checkbox']:checked").each(function(idx, el){
    days.push($(el).data("dayOfWeek"));
  })
  return days;
}
</script>