Will new quote tweet available to third party Apps via REST API?
What exactly are you referring to?
Have a look at Method to retweet with comment
quoted status is like this
I don’t find this api documents from the developer site
i just find it, put the quoted status url in attachment_url arg, e.g.
Tweet.update('cool', attachment_url: 'https://twitter.com/emorima/status/1061581991798169600' )