Filtering the post list in the admin area

I would suggest using post_submitbox_misc_actions action as shown in the below example to provide an option for Publish meta-box.

<?php

add_action( 'post_submitbox_misc_actions', 'my_post_submitbox_misc_actions' );

    function my_post_submitbox_misc_actions(){
    ?>
    <div class="misc-pub-section my-options">
        <label for="my_custom_post_action">My Option</label><br />
        <select id="my_custom_post_action" name="my_custom_post_action">
            <option value="1">First Option goes here</option>
            <option value="2">Second Option goes here</option>
        </select>
    </div>
    <?php
    }

    ?>

Once used for at-least one post( or a CPT), then those options should appear beside publish actions in all posts admin page.