Add attribute target="_blank" to all links children of "posts-in-sidebar" class.

functions.php

<?php
/**
 * Register scripts.
 * Add this function to your functions.php file or to your functions plugin.
 *
 * @since 1.0.0
 */
function posts_in_sidebar_hacks() {
	wp_register_script(
		'pis_scripts',
		get_stylesheet_directory_uri() . '/scripts/pis-hacks.js',
		array( 'jquery' ),
		'1.0.0',
		true
	);

	wp_enqueue_script( 'pis_scripts' );
}
add_action( 'wp_enqueue_scripts', 'posts_in_sidebar_hacks' );

pis-hacks.js

/**
 * Add the `target="_blank"` attribute to Posts in Sidebar links.
 * Activate one of them only (LINE A or LINE B), according to your needs!
 */

jQuery(document).ready(function(){
	// Add the `target="_blank"` attribute to all links of Posts in Sidebar.
	// Targets any link child of .posts-in-sidebar class.
	// Deactivate this line, in you want line B, prepending a double slash (//) in front.
	// Line A:
	jQuery('.posts-in-sidebar a').attr('target','_blank');

	// Add the `target="_blank"` attribute only to Posts in Sidebar title links.
	// Targets any link with .pis-title-link class.
	// Deactivate this line, in you want line A, prepending a double slash (//) in front.
	// Line B:
	jQuery('a.pis-title-link').attr('target','_blank');
});