What's the problem?

It is impossible in JIRA to restrict issue access to the employees of particular company. It is because JIRA doesn't know what is a "company". There is no such entity.

Existing solutions

As a workaround you can try to use Zones plugin. However, it implements "company" entity as JIRA group. But it complicates managing companies and doesn't give you a full-value entity of a "company".

Solution using CRM for JIRA

If using CRM for JIRA you can configure a company dictionary in JIRA. That will allow you to define a Company in the issue custom field mannually, or auto completing it by issue reporter.

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