How to inctercept the custom page content?

In theme folder I’ve created ‘page-mycustom.php’ with custom html code for that page.

I want to intercept that content with a filter, but I only target Default pages. How to get get it to work on custom pages also?

function custom_page_content_filter($content) {
	return "Modified Content";     
}

add_filter('the_content', 'custom_page_content_filter');