请尝试以下代码

/* push data from request */
function pushDataToDropdown() {
  let select = $('#sortByTag');

  let parentMarkupObj = {
    'markup': `<option>1212123</option>`
  };

  select.append(parentMarkupObj.markup);
}

/* add popover to select items */
function addOptionsDropdownToTags() {
  let allTagInFilter = $('.dropdown-menu.inner li');

  /* непосредственно вставка дропдауна для каждого пункта селекта */
  allTagInFilter.append('<button type="button" class="custom-popover" data-toggle="popover" title="Popover title" data-content="Popover">Popover btn</button>');
}

window.addEventListener('DOMContentLoaded', (event) => {
  pushDataToDropdown();
  setTimeout(function() {
    $('select').selectpicker('refresh');
  }, 500)
  setTimeout(function() {
    $(document).on('click', '.bootstrap-select', function (e) {
      e.stopPropagation();
    });
  }, 650)
  setTimeout(addOptionsDropdownToTags, 800);
});

将此代码$(document).on('click', 'someyourContainer .dropdown-menu', function (e) {更改为$(document).on('click', '.bootstrap-select', function (e) {