Looking for an on-premise ticketing tool service

[Mduduzi Ndlovu]

I am looking for a support tool I can use for my clients to send their requests or tickets through one mailbox.

I have three admin users that will be using the system, I would like to find out the following.

1. How much would it cost for three user licenses?
2. What would be the implementation of the system?
3. What is the start-up fee?
4. What would be the maintenance fee?
5. What would be the monthly cost?  

[Nic Brough -Adaptavist-]

Service Desk can do that happily.

1. Depends on your users.  If they're going to be just "customers" (send, update and report on their own calls), nothing.  If they're going to be Agents, quite a lot. 
2. You install it on a server that can run Java and is on your network, with a database behind it, then use it via a browser.  I'm not sure quite what you're looking for with that question
3. and 4 and 5, and part of 1 - see https://www.atlassian.com/software/jira/service-desk/pricing?tab=host-on-your-server