"Email Your Reply" , can be present when replying to a ticket as an agent: 

By default this should be checked ON.  If turned OFF, your requester (user or customer that submitted this ticket) will NOT receive this reply. 

Note: This will NOT stop any other email templates from being sent.  For example, if you un-checked this option, the current reply won't go out, but other email templates like Ticket Closed emails could still go out, if enabled.

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