Page showing posts from one category only

for example, in a child theme http://codex.wordpress.org/Child_Themes of Twentyfourteen, create a custom page template http://codex.wordpress.org/Page_Templates, based on page.php;

replace that section:

<?php
				// Start the Loop.
				while ( have_posts() ) : the_post();

					// Include the page content template.
					get_template_part( 'content', 'page' );

					// If comments are open or we have at least one comment, load up the comment template.
					if ( comments_open() || get_comments_number() ) {
						comments_template();
					}
				endwhile;
			?>

with a custom query and loop, calling just posts of the special category.

for some coding ideas, have a look at http://codex.wordpress.org/Page_Templates#A_Page_of_Posts

http://codex.wordpress.org/Class_Reference/WP_Query
http://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters