I've got a horizontal menu for wordpress site and also the menu products are groups. On clicking each food selection , I ought to show latest publish for particular category.

e.g.

Item_1 Item_2 Item_3 Item_4 are my menu products. The like clicking Item_2, I ought to show latest publish for your group of Item_2. Is possible in Wordpress? I'm only a newbie to wordpress, will appreciate any help.

Yes it's how wordpress works. Except, you need to produce the groups inside your admin dashboard and specify the kitty you would like when you're writing your publish.

If you want info regarding how to develop a template file, you need to read http://codex.wordpress.org/Category_Templates

which explain crafting wordpress query.