I am currently using JIRA Core and I can configure Versions and Components for my project using project administrator page.
But I am not able to assign any issue to a component or fixversion.
Am I missing something or do I need JIRA Software also to make use of component and version?
They're part of JIRA Core, not Software.
Make sure the fields are on the edit screen and try editing the issue - the fields will appear and you will be able to select options for them (assuming you have "edit issue" rights in the project)
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