You can easily customize all ticket email templates by going to Setup -> Email Templates -> Tickets

Here is a list for all ticket email templates:

• New Ticket Opened (Opened by staff, sent to customer) – (Sends to customer when ticket is opened from admin area)
• Ticket Reply (Sent to customer) – When admin add ticket reply this email will be sent to the customer.
• Ticket Reply (Opened by customer sent to staff members) – When client reply to ticket and an email will be sent to all staff member which department is the same like the ticket department.
• New Ticket Open Autoresponse – (When client open new ticket autoresponse message)
• New Ticket Created (Opened by custom, sent to staff members) – (When new ticket is opened by customer all the staff members which department is the same like the ticket department receives this email)
• Auto Close Ticket – This email will be sent when cron auto closes the ticket.

Feel free to disable any of the email templates if you don’t want to be sent.