how to make special modal for each post

Question

Yes it is possible. I think you are using bootstrap modal. And it is looks like this:
Bootstrap Modal

<!-- Button trigger modal -->
<button type="button" class="btn btn-primary" data-toggle="modal" data-target="#exampleModal">
    Launch demo modal
</button>

<!-- Modal -->
<div class="modal fade" id="exampleModal" tabindex="-1" role="dialog" aria-labelledby="exampleModalLabel" aria-hidden="true">
    <div class="modal-dialog" role="document">
        <div class="modal-content">
            <div class="modal-header">
                <h5 class="modal-title" id="exampleModalLabel">Modal title</h5>
                <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                    <span aria-hidden="true">&times;</span>
                </button>
            </div>
            <div class="modal-body">
                ...
            </div>
            <div class="modal-footer">
                <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>
                <button type="button" class="btn btn-primary">Save changes</button>
            </div>
        </div>
    </div>
</div>

And now you see it works with special ID and special data-target So you must give special ID and data-target for each modal.

Let’s create new query with speacial modals.

<?php
// Custom WP query query
$args_query = array(
    'order' => 'DESC',
);

$query = new WP_Query( $args_query );

if ( $query->have_posts() ) {
    while ( $query->have_posts() ) :
        $query->the_post(); ?>
        <!-- Button trigger modal -->
        <button type="button" class="btn btn-primary" data-toggle="modal" data-target="#exampleModal-<?php echo esc_attr( get_the_ID() ); ?>">
            Open "<?php the_title(); ?>" Modal
        </button>

        <!-- Modal -->
        <div class="modal fade" id="exampleModal-<?php echo esc_attr( get_the_ID() ); ?>" tabindex="-1" role="dialog" aria-labelledby="exampleModalLabel" aria-hidden="true">
            <div class="modal-dialog" role="document">
                <div class="modal-content">
                    <div class="modal-header">
                        <h5 class="modal-title" id="exampleModalLabel">Modal title</h5>
                        <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                            <span aria-hidden="true">&times;</span>
                        </button>
                    </div>
                    <div class="modal-body">
                        <?php the_content(); ?>
                    </div>
                    <div class="modal-footer">
                        <button type="button" class="btn btn-secondary" data-dismiss="modal">Close</button>
                        <button type="button" class="btn btn-primary">Save changes</button>
                    </div>
                </div>
            </div>
        </div>
<? endwhile; } else {
    echo 'No posts found';
}
wp_reset_postdata();

?>