Make all posts of a category to only appear on the sidebar of that particular page

I have created a top navigation menu based on categories and assigned all posts to different categories. What I want is for each "page" to only show posts from that category. For example I have 5 posts in "Home" and 10 posts in "Articles". I want the Home page to show 5 posts on the sidebar and show 10 posts in the Articles page.

I have tried different widgets such as wp-posts-widget but these only list either all posts from all categories or show categorised posts on ALL pages.

Please help