<?= $form->field($model, 'companies_company_id')->dropDownList(
  \yii\helpers\ArrayHelper::map(\backend\models\Companies::find()->all(),'company_id','company_name'),
  [
    'prompt'=>'select Company',
    'onchange'=>'
      $.post("index.php?r=branches/lists&id='.'"+$(this).val(),function(data){
        $("select#departments-branches_branch_id").html(data);
      });',
  ]
) ?>
<?= $form->field($model, 'branches_branch_id')->dropDownList(
  \yii\helpers\ArrayHelper::map(\backend\models\Branches::find()->all(),'branch_id','branch_name'),
  [
    'prompt'=>'Select Branches',
  ]
) ?>

public function actionLists($id)
{
  $countBranches = Branches::find()
    ->where(['companies_company_id' => $id])
    ->count();
  $branches = Branches::find()
    ->where(['companies_company_id' => $id])
    ->all();
  if ($countBranches > 0) {
    foreach ($branches as $branche) {
      echo "<option value='" . $branche->branch_id . "'>" . $branche->branch_name . "</option>";
    }
  } else {
    echo "<option>-</option>";
  }
}