Now, Twitter lets you control who replies to tweet: Here is how it works
After testing with a select users, Twitter has incorporated the conversation moderation feature that lets you control who replies to you tweet. The new feature is now available on Twitter for iOS, Android and web client. All accounts, including those of elected officials, can now select the people who will be allowed to reply while composing a new tweet, according to Twitter.
The feature allows Twitter user to set the reply preference before posting a tweet. Users can choose from three options: everyone (the default setting), only people you follow, or only people you mention. Tweets with the latter two settings will be labeled and the reply icon will be grayed out. However, people will still be able to view, retweet, retweet with comment, and like such Tweets.