Two options I would suggest.
1) When opening a task board you have several filters on top of your task board. On the left top of your screen you will see your Jira Project name followed by a filter name (e.g. "On the fly"). Below there are three filters that are depending on each other.
First one should be Task Board in your case. The second filter (to the right of "Task Board") is reserved for the version. Make sure that is set to the Version you would like to get displayed on your screen, e.g. "Unscheduled". Finally, there is a filter for assignees.
I assume that you should change the version filter to get your result.
2) In the task board configuration you can apply some additional filter options. For instance, you can tell Jira to filter for a certain resolution. This can be applied to any column. So, maybe you want to filter for issues that have NO explicit resultion set so far, independent of their fix version.
Update: There is even a third option.
3) I assume that you are using the default value for your Task Board like "On the fly". Go to "On the fly" and click the arrow that is to the right of this subject. When you click "Manager" you will see a screen with different configuration options. Go to "Filter". Check your filter -> maybe it is using "None".
So, you should create a new filter first that is filtering for all issues that are not versioned yet. Apply your Task Board to this filter.
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