I am trying to make a field show and save from quickedit screen

You have to register your quick edit custom box:

function display_custom_quickedit_book( $column_name, $post_type ) {
    // it would be a good idea to add a nonce here
    ?>
    <fieldset class="inline-edit-col-right inline-edit-book">
      <div class="inline-edit-col column-<?php echo $column_name; ?>">
        <label class="inline-edit-group">
        <!-- here goes your input -->
        </label>
      </div>
    </fieldset>
    <?php
}
add_action( 'quick_edit_custom_box', 'display_custom_quickedit_book', 10, 2 );

And then you have to process the input value while saving post. But if that field is already a custom box, then you’ve already modified save_post to process it, I guess…

And there are a few more tricks with setting values and so on. You can read more on that on Codex: https://codex.wordpress.org/Plugin_API/Action_Reference/quick_edit_custom_box