How to create a button on module configuration page that calls a custom php function? I am creating a custom module that has a button on the module's configuration page. When the button is clicked, a custom php function (located in the custom_module.module file) needs to run to perform some task. 

How can I create a button on the custom module's configuration page that allows me to click the button to manually run the custom php function?
You should use the Drupal Form API for it.

Please, check it: https://api.drupal.org/api/drupal/developer!topics!forms_api_reference.html/7#submit (it is about adding button).

And it: https://api.drupal.org/api/drupal/developer!topics!forms_api_reference.html/7#submit_property (it is about run custom function).