Custom field as featured image caption

Here’s one way to inject the custom field as the featured image caption with help of the post_thumbnail_html filter:

add_filter( 'post_thumbnail_html', function( $html, $post_id )
{
    if( $html && $caption = get_post_meta( $post_id, 'wpcf-bildunterschrift', true ) )
        $html .= sprintf( '<p>%s</p>', sanitize_text_field( $caption ) );

    return $html;
}, 10, 2 );

Hopefully you can adjust this to your needs.

Update

According to ticket #12235 we will have a new template tag, in WP 4.6+, to display featured image caption, namely:

the_post_thumbnail_caption()

where it’s output is filterable through the the_post_thumbnail_caption filter.

It’s a wrapper for the function:

get_the_post_thumbnail_caption()

That’s again wrapper for the function:

wp_get_attachment_caption()

This function fetches the caption from the attachment’s post_excerpt field and it’s output is filterable through the wp_get_attachment_caption filter.

Example

If our theme used this new template tag, then we could filter it with:

add_filter( 'the_post_thumbnail_caption', function( $caption )
{
    if( $custom = get_post_meta( get_the_ID(), 'wpcf-bildunterschrift', true ) )
        $caption = sanitize_text_field( $custom );

    return $caption;
}, 10, 2 );

Note that here we e.g. strip out the possible HTML tags from the custom field. If you want to support HTML then you can check out the discussion in the ticket.

Update

Example

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