Adding a new menu item to admin/config page of Drupal 8

This is fairly straight forward and there is no any special thing to do compared to traditional menu items. So here is how you do it.

First you need a routing defined. Here is a great example of how you add a routing to your config form https://www.drupal.org/docs/8/api/configuration-api/working-with-config….

So from that example: 

example.routing.yml is looks like below ("example" is the module name).

example.settings:
  path: '/admin/structure/example/settings'
  defaults:
    _form: '\Drupal\example\Form\exampleSettingsForm'
    _title: 'example'
  requirements:
    _permission: 'administer site configuration'

Now add another file called example.links.menu.yml ("example" is the module name).

example.settings:
  title: 'My Title'
  parent: system.admin_config_services
  route_name: 'example.settings'

Parent is important here:

For "Web Services":

parent: system.admin_config_services

For "Regional And Language":

parent: system.admin_config_regional

Other possible values for Parent:

parent: system.admin_config_media
parent: system.admin_config_development
parent: system.admin_config_search
parent: system.admin_config_system
parent: system.admin_config_ui
parent: system.admin_config_content