Public issue tracker tool with Jira integration

Hi everyone. I am searching for a tool to use as a public issue tracker. We are using Jira to create and track bugs internally but want to make certain bugs public. Therefore this tool needs to have a jira integration. If a ticket in jira is created, this should automatically create an entry in that issue tracker. If a jira ticket is updated, that updated data should sync to the issue tracker as well. We are having a hard time to find a tool that fits.

Is anyone aware of something like this or is it time to develop our own?