Adding your own custom Quote fields to a cloned quote upon cloning is as simple as creating a "Field Set" and creating a new Button on the Quote. For more info on creating Field Sets, see the Salesforce documentation.
First, create a field set on the Quote Object. In this case, we simply called it "Clone".
Add the following to the url:
&fs=THENAMEOFYOURNEWFIELDSET
Replace THENAMEOFYOURNEWFIELDSET with your newly created Field Set. In the example, we're using the "Clone" Field Set we created, so we'll adjust our URL to be:
/apex/tysoxrr__CloneQuote?id={!Quote.Id}&fs=clone
Save the button, and add it to your page layout.
| NOTE: You can have multiple field sets and different buttons based on your process so that the correct fields are copied over depending on the button used. |