Conditional Tags for specific category of custom posts

Try using has_term() which accepts a term_name, term_id, or slug to test again. You’ll need to pass the post_id too, something like this:

global $post;

if( isset( $post ) && is_singular( 'my_custom_post_type' ) && has_term( 'my_custom_post_type_category', 'my_custom_taxonomy', $post->ID ) ) {
    // Code Goes Here...
}

You may also be able to use has_category() which work very similar but if I were a betting man I’d bet that that function would only work for the built-in Post Categories but still worth mentioning.