No, you don't get any notification or message when someone has quoted a post of yours. The only way you can find it out is if you regularly check the threads you posted in. Subscribing to threads partially helps with this.
It has been suggested a few times we get a quote notification system, however it's up to Zise and Versuvio to decide whether such a plugin is installed or not. So far it was deemed too much of a hassle based due to the amount of posts and threads made on NB, but as I said it's up to the head admins.