How to show only Specific Categories on Custom Pages in Wordpress

Method -1

$args = array(
    'hide_empty' => 0, //Show me all the categories, even the empty ones
    'orderby' => 'count', //which accepts a string. You can pick from the following options: ID to order the categories by their ID (no, really?), name to sort them alphabetically (the default value), slug to sort them in the alphabetical order of their slugs, and count to order by the number of posts they contain.
    'order' => 'DESC', //The chosen order can be reversed by setting DESC (descending) as a value for the order option (by default this option is set to ASC (ascending)).
    'include' => '15,16,9'
);

wp_list_categories($args);


Method - 2

$categories = get_categories( array(
    'orderby' => 'name',
    'order'   => 'ASC',
    'include' => '15,16,9'
) );

foreach( $categories as $category ) {
    $category_link = sprintf( 
        '<a href="%1$s" alt="%2$s">%3$s</a>',
        esc_url( get_category_link( $category->term_id ) ),
        esc_attr( sprintf( __( 'View all posts in %s', 'textdomain' ), $category->name ) ),
        esc_html( $category->name )
    );

    echo '<p>' . sprintf( esc_html__( 'Category: %s', 'textdomain' ), $category_link ) . '</p> ';
    echo '<p>' . sprintf( esc_html__( 'Description: %s', 'textdomain' ), $category->description ) . '</p>';
    echo '<p>' . sprintf( esc_html__( 'Post Count: %s', 'textdomain' ), $category->count ) . '</p>';
} 


Credit- https://stackoverflow.com/a/45729730/7162602