EDIT: I'm adding code so that it can help:

in functions.php

//  AJAX HOOKS TO LOAD PRODUCTS' INFO
add_action('wp_ajax_get_product_info', 'get_product_info' );
add_action('wp_ajax_nopriv_get_product_info', 'get_product_info' );

// SHOULD RUN SHORTCODE TO GET PRODUCT INFORMATION AND SEND IT BACK TO JS SCRIPT
function get_product_info() {
   //Checks the nonce and kills the script if wrong
   $nonce = $_POST['nonce'];
   if ( ! wp_verify_nonce( $nonce, 'return_posts' ) )
        die ( 'Wrong nonce!');
   //Process Info
   $pid = $_POST['product_id'];   
   header('Content-type: text/html');
   
   // Returns the shortcode
   echo do_shortcode("[ps_product_list id_product=".$pid." tpl=product-grid-exclusives.tpl]");

    // We don't want anything else to run
   exit;
}

// REGISTERS, LOADS & LOCALIZES product-store-ajax.js
if (!function_exists('load_scripts')) {
    function load_scripts() {
                
        if ( !is_admin() && is_category('teaser-online-exclusives') ) {
                
                wp_register_script( 'product-ajax', get_stylesheet_directory_uri().'/js/product-store-ajax.js', array( 'jquery' ), '', true );
                
                wp_enqueue_script('product-ajax');
                
                wp_localize_script( 
                    'product-ajax', 
                    'productajaxvars', 
                    array( 
                        'ajax_url' =>  admin_url( 'admin-ajax.php' ), 
                        'nonce'    =>  wp_create_nonce( 'return_posts' ),
                        'callback' => 'get_product_info'
                    ) 
                );
        }
    }
}
add_action('wp_enqueue_scripts', 'load_scripts');

And the JS file:

(function( $ ) {
    $(function() {
      
        $.ajax({
            url:  productajaxvars.ajax_url,
            data: { 
                action:  productajaxvars.callback,  // callback defined in functions.php
                nonce :  productajaxvars.nonce,
                product_id: 82},
                success: function( response ) {
                            alert(response);
                },
                type: "POST",
        });
         
              
    });
})( jQuery );