OK @Muyassir S. - we are missing some information to understand the problem.
We basicly dont know if the "page" you are talking about is a category page, Your home page or a custom page - meaning: which file is being used to show that blog?
here are two possible solutions.
If we are talking about a category / page with slug:
if(is_category('blog')) {
// add whatever you want here
}
- should be placed inside category.php template
If you went to: Settings > Reading
and set the posts page over there then its a page and can be accesses like this.
$blogPgid = get_option('page_for_posts');
if(get_the_ID() == $blogPgid) {
// add whatever you want here
}
- should be placed inside page.php template.
Let me know if this helps
EDIT 1:
here is what i would do.
1st. Just copy page.php in your theme and name the new copy page-blog.php Now, add a in the top of that page these tag (above everything).
<?php
/*
Template Name: Blog Page
*/
?>
2nd. go back to that page in WP admin and pick that page template. Now you have a page / file that you can control and add whichever specific stuff you'd like.