Can’t get custom CSS file to load in Child theme

A few points:

First:

You are using is_page_template() on the “‘page-sgt_peppers.php” enqueue then you use is_page() for “page-mp3-downloader.php”.

You should use is_page_template() for both.

Second:

You are using wp_register_style() incorrectly. From the codex:

A safe way to register a CSS style file for later use with
wp_enqueue_style().

Note the “later use” part. The register script function allows you to call wp_enqueue_style($handle); later on instead of listing paths and dependency over and over. You do not have to register them at all but it is good practice so I am keeping it in my suggested fix below.

You should also register them with unique handles. Codex:

$handle (string) (required)Name of the stylesheet (which should be unique as it is used to identify the script in the whole system).

That said you can try the following:

<?php

/* This enqueues the Parent style.css file for this child theme */
function my_theme_enqueue_styles() {

    $parent_style="twentyseventeen-style"; // This is 'twentyseventeen-style' for the Twenty Seventeen theme.

    wp_enqueue_style( $parent_style, get_template_directory_uri() . '/style.css' );
    wp_enqueue_style( 'child-style',
                      get_stylesheet_directory_uri() . '/style.css',
                      array( $parent_style ),
                      wp_get_theme()->get('Version')
    );

    /*Register styles for later use*/
    wp_register_style('wpsx-custom-style', get_stylesheet_directory_uri() . '/custom.css');
    wp_register_style('wpsx-reset-mp3-style', get_stylesheet_directory_uri() . '/css/reset-mp3.css');
    wp_register_style('wpsx-main-mp3-style', get_stylesheet_directory_uri() . '/css/main-mp3.css');



}
add_action( 'wp_enqueue_scripts', 'my_theme_enqueue_styles' );

/*=============  Code Added by Me ======================================- */

/* Code to enqueue(load) the custom.css file for sgt. peppers page */
function wpb_adding_styles() {
    if (is_page_template('page-sgt_peppers.php')) {
        wp_enqueue_style('wpsx-custom-style');
    }

    /* Load style sheets for MP3 Downloader page if  page requested */
    if (is_page_template('page-mp3-downloader.php')) {
        wp_enqueue_style('wpsx-reset-mp3-style');
        wp_enqueue_style('wpsx-main-mp3-style');
    }

}

add_action('wp_enqueue_scripts', 'wpb_adding_styles');