Using Taxonomy Order Plugin

If you are using the Category Order and Taxonomy Terms Order you can use this code to use the order of that plugin and the images:

<?php
		$terms = apply_filters( 'taxonomy-images-get-terms', '', array(
			'taxonomy'=>'MY_CUSTOM_TAXONOMY',
			'image_size' => 'thumbnail',
			'term_args'    => array(
				'orderby'		=> 'term_order',
				'hide_empty'	=> 0,
				'child_of'		=> 3
				),
			) );

		echo '<ul>';
		foreach( (array) $terms as $term){
				  echo '<li>';
				  echo '<a href="' . esc_url( get_term_link( $term, $term->taxonomy ) ) . '">' . wp_get_attachment_image( $term->image_id, 'thumbnail' ) . '<h4>'. sprintf(__('%s', 'my_localization_domain'), $term->name) . '</h4>' . '</a>';
			  	  echo '</li>';
			}
		echo '</ul>';
	?>

Hope it helps! ??

https://www.ads-software.com/plugins/taxonomy-images/