Hi @Mars ,
assuming that you have SCOM 2019 you need to consider a couple of things:
What gets send where is controller by the subscription as you know, so if you want to send some of the alerts (from specific rules or monitors) over another channel, you have to create the channel itself in advance and then configure the subscription criteria. In my opinion this article gives you a nice overview of all the options and possibilities:
How to create notification subscriptions
https://learn.microsoft.com/en-us/system-center/scom/manage-notifications-create-subscriptions?view=sc-om-2019
You can control also what gets send, using the alert name, like depicted by Leon here:
SCOM - Alert Basics
https://www.cookdown.com/blog/scom-alert-basics
You can always open a rule or the monitor check its targeted class and configure the class in the subscription. that would also help you filter and pick only the alerts that you need.
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Regards
Stoyan Chalakov