Adding system field onto a screen through REST API

I am creating a project using REST API and Epic, Story, Task and Sub-tasks under the project.
**’/rest/api/2/project’, ‘POST’ **

But I am facing issues for the specific field or IssueType that are not available on the screen.

If I use a simple software project template that it showing IssueType Story not available on the screen. Or if I go with Scrum or Kanban template than DueDate, TimeTracking and Report, Assigned missing from the screen.

ProjectTemplateType [
**com.pyxis.greenhopper.jira:gh-simplified-agility-kanban **
**com.pyxis.greenhopper.jira:gh-simplified-agility-scrum **
**com.pyxis.greenhopper.jira:basic-software-development-template **

Please help to how templates work with default fields/IssueType available on screen?
Or How we can check field availability on screen and add that on screen?