List user comments in author page

Try with WP_Comment_Query and make sure you have the right Author ID from the Author Template.

// WP_Comment_Query arguments
$args = array (
    'user_id'        => $user->ID,
    'post_status'    => 'approve',
    'number'         => '10',
);

// The Comment Query
$comments = new WP_Comment_Query;
$comments = $comments->query( $args );

// The Comment Loop
if ( $comments ) {

    $output.= "<ul>\n";

    foreach ( $comments as $c ) {
        $output.= '<li>';
        $output.= '<a href="'.get_comment_link( $c->comment_ID ).'">';
        $output.= get_the_title($c->comment_post_ID);
        $output.= '</a>, Posted on: '. mysql2date('m/d/Y', $c->comment_date, $translate);
        $output.= "</li>\n";
    }

    $output.= '</ul>';

    echo $output;
} else {
    echo 'No comments found.';
}