You probably have an ''Enterprise'' license.
You can only create real ''Template'' projects with a Premier/ALM license.
Perhaps the term ''template'' is at issue here.
If you intend to use a project as the basis (copy for a starting point) for other projects - let's call it a ''base project'', just create a domain with a name like ''base projects'' - just to remind you that the project is for copying. You can have a series of these, but do not allow users to access them, you may want to get the group security setup ahead of time and leave users out of the group lists. If you want to setup user lists, the users will have access and could possibly start working in them, so you may want to keep them inactive.
Then you can maintain the project going forward with all of your current customizations -- but you do not use it for production, just as a base for copying.
When you need to make a NEW project, you pick the right ''base'' project, and do a ''create Project/Create a project by copying data from an existing project'', select all objects/entities, and you have a NEW project that is the same as your base.
The copied projects do not know anything about where they were created - they WILL NOT update with any new customizations seen on the BASE, that must be done manually (this is why a different, and more expensive, license is required for ''real templates'').