I am using Kanban methodology in Jira to manage the workflow of a 'mature' project. We can do deployments to production on Thursdays, so we accumulate stories in the 'Ready For Production' column until they go in a release, and then, after they are deployed, we hit the 'Release' button and create a new version. However, if, let's say we're on a Monday and something needs to be released urgently and we create an expedite swimlane, is there any way to release just that and not the other non-expedite tasks that are due to be released on Thursday?
When you click the "Release" button on a company-managed Kanban board, you are choosing from a list of versions that are allocated to issues in that column. When you don't have versions assigned to those issues, you would be releasing all of them.
If you set the Fix Version field in those issues appropriately, you will be able to release one version and mark the issues associated with that version as Released. It's not clear what happens if you have some issues with a manually set Fix Version and others with no Fix Version, so you may need to explicitly set the Fix Version of all of the issues in the column.
I would also recommend looking at your issue workflow in general and consider setting the Fix Version field in advance. You can unlock some good visualizations of progress toward a version and make sure the work that you expect to release is on track for completion throughout the development process.