As things are, the Twitter mobile app can ping you with alerts for all the tweets posted by an individual account, but the new feature in testing adds an extra level of granular control by notifying you only of replies to a particular tweet.
The option is designed to make following the development of a conversation related to a specific tweet more straightforward, as this can sometimes be difficult if you don't already follow the original poster.
You probably have notifications on for your must-follows. Now you can get notifications when there’s a new reply to a Tweet you’re interested in! We’re testing this on iOS and Android now. pic.twitter.com/MabdFoItxc— Twitter (@Twitter) August 8, 2019
The news follows several other features that have recently been trialed or rolled out on the social media platform, all with the aim of handing over more control to users and creating a "healthier service" by cutting down on abuse and harassment.
They include a snooze button to temporarily silence notifications from the app, and a Hide Replies feature that lets users collapse replies to their tweets. The latter is designed to allow users to moderate conversations by keeping them on topic and hiding trolls where necessary.