How to notify many users of a new post on Twitter?

Question

Twitter

There is a problem: we have a new tweet, about which we need to notify N number of users, let's say 10. Not all of them are subscribed to me. The most trivial method is mentions, but it hits the character limit on twitter. Another method is a special private messaging system, but it only works if the user is following me.
So far, there is such a plan: with a frequency of several hours, repeat a tweet with new mentions, but this pollutes the feed. Another condition is to work through the Twitter API.
Has anyone dealt with such a problem?