Display movies that apear this day next

What you want to do in this case is to use a meta_query in WP_Query like the following. You can reference the following Codex for more information https://codex.wordpress.org/Class_Reference/WP_Query#Custom_Field_Parameters. Once you have the posts. Loop over them and add their date as data attribute, and filter the items using data attributes.

$args = array(
    'post_type' => 'post',
    'meta_query' => array(
        array(
            'key'       => 'premiera_cinema',
            //Beginning and End date in format of YYYYMMDD
            'value'     => array( 20130101, 20130107 ),
            'type'      => 'date',
            'compare' => 'BETWEEN'
        )
    )
);
$query = new WP_Query( $args );