Additional field settings without creating a new field type
This works for me:

$field-&gt;setThirdPartySetting('mymodule', 'my_checkbox', $form_state-&gt;getValue('my_checkbox'));


After you save your field settings, the new third party setting should be available in your field config:

third_party_settings:
  mymodule:
    my_checkbox: 1


Here is a good article about this: https://www.webomelette.com/drupal-8-custom-data-configuration-entities-using-thirdpartysettingsinterface