Twitter has a feature where users can ‘mute notifications from people’ by selecting various filters.
Checking these filters will allow you to block notifications from certain Twitter handles – accounts which have a default profile photo, accounts which do not have a verified email address or contact number.
Twitter also lets users filter notifications from accounts they do not follow, and new Twitter users.

Some Twitter users rejoiced at the opportunity of muting ‘Sanghi trolls’ from their timeline.
Want to keep your Twitter timeline clean from Sanghi Trolls? Make these changes in your notification settings. pic.twitter.com/QwAjF4474Y
— Kapil (@kapsology) July 30, 2018
And if certain trolls manage to slip through these filters, the Mute and Block options always come in handy.