If you want to send an email to a mentioned user, then we do not support it directly, but it is possible to achieve it in Jira:
- a user can use Jira Search for checklist items containing his/her mention (see the third bullet in the linked docs): https://gebsun-support.atlassian.net/wiki/spaces/IC/pages/774471744/Search+advanced+with+JQL
- user can save it as a filter and subscribe to it (so Jira will send notifications): https://confluence.atlassian.com/jira064/receiving-search-results-via-email-720416706.html?_ga=2.147813495.1712339118.1559117577-1941309080.1504852851#ReceivingSearchResultsviaEmail-SubscribingtoaFilter