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// Ref - https://codex.wordpress.org/Plugin_API/Filter_Reference/ajax_query_attachments_args

add_filter( 'ajax_query_attachments_args', 'show_current_user_attachments', 10, 1 );

function show_current_user_attachments( $query = array() ) {
    $user_id = get_current_user_id();
    if( $user_id ) {
        $query['author'] = $user_id;
    }
    return $query;
}