Query posts from a specific category and selected tag

Since you’re working with the tag archive index page query, this really won’t be all that difficult. You simply need to filter the query parameters at pre_get_posts, using your criteria.

For example:

function wpse137627_pre_get_posts( $query ) {
    // If this is the tag archive index,
    // and is the main query
    if ( is_tag() && $query->is_main_query() ) {
        // Limit the query to the specified category
        // Change '123' (int) to the appropriate category ID
        $query->set( 'cat', 123 );
    }
}
add_action( 'pre_get_posts', 'wpse137627_pre_get_posts' );

You can also pass the category slug, using $query->set( 'category_name', 'cat-slug' ).