How we can get custom field type which will bring custom data from custom table to use as a drop down
You might want to look at http://materializecss.com/badges.html#dropdown The have a pretty straight forward way of creating a dropdown menu, including code examples.

If it's for a certain Form ID you can use hook_form_FORM_ID_alter to specify which ID and alter it's HTML inside $form_state. If you don't know it's structure you can var_dump($form_state); first instead so you know what to alter.

P.S. also add the CSS of course: drupal_add_css(drupal_get_path('theme', 'custom') .'https://cdnjs.cloudflare.com/ajax/libs/materialize/0.97.1/css/materialize.css', 'theme', 'screen,projection', FALSE);