If I understand well, you have a page template, and you want to use this page template as a category archive.
The term to show is in a page meta field with key ‘cat_page’.
If I’m right, in this page template use:
the post(); // being a singular page the 'while' stuff is useless
the_content(); // this will show the page content
$cat = get_post_meta( get_the_ID(), 'cat_page', true ); // get the category to display
if ( $cat ) { // if category is setted in page custom field
$query = new WP_Query( 'category_name=" . $cat ); // run the custom query
while ( $query->have_posts() ) { $query->the_post(); // run the custom loop
// your post loop code goes here
}
wp_reset_postdata(); // reset the post data after the custom query
}
Pleas note that to make this work in the custom meta "cat_page' you should put the category slug (not the category name).