How to show user’s own post in a specific page

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Try using wp_query

Here is the codex link:

WP_Query – Docs – WordPress

Here is an example of something that may help:

global $current_user;
      get_currentuserinfo();
$authorID = $current_user->ID;
    $args = array(
              'post_type' => 'post',//or whatever you need
              'posts_per_page' => 5,
              'author' => $authorID
              );

    $temp = $wp_query;
    $wp_query= null;
    $wp_query = new WP_Query($args);

You could use this in you own template page to display only the current user’s posts.