Twitter introduce a new features to it's mobile app that will make your experience much better, it will give you control over what you see and who you interact with on Twitter.
Two simple settings to give you better control over your Twitter experience. https://t.co/pEJuMUhCYs pic.twitter.com/jmFd0rDoV6— Twitter Support (@Support) August 18, 2016
With this update you'll be able to limit your notification, you can control whose notifications you want to see by turning on "Only People You Follow" toggle button. This won't make any impact on your twitter experience it will continue unchanged.
As for now this update is only seen in iOS app, we hope this feature will come to Android devices soon.