What options are in-place to prevent a User in modifying a user story they are not assigned and belong to a different scrum team than owned by the user story?
For permissions in Jira Align, you can control whether or not a user has access to edit a work item (e.g. Story) based on their system role. For each system role you can give some people access to edit specific work item types and some read-only access. The caveat is that it's a universal thing...if you can edit you can edit all of those work items of that type (e.g. Story) or none of them (within the Portfolio you are part of). Based on your post I'm guessing you're looking to prevent a person on one team from editing the work on another team (even if they have the same system role and are within the same portfolio), which is not possible today. We do have pretty robust audit logs in Jira Align, so if someone does modify another teams issue (when they shouldn't), you will be able to see this in the audit log.
Here's some additional info on permissions (if you'd like to learn more):
Also, if you'd like to submit an enhancement idea for this, here's an article that show you how to submit an idea through the Jira Align ideation portal:
Thanks and let me know if you have any questions.
Assuming you are using Jira at the story level, then your boards should be representing teams, with a single project underlying each one. You can therefore set permissions on the projects that say "only members of this team can edit the issues"
My answer is only useful if you are using Jira Software coupled with Jira Align. If you are only using Align, please do ignore this thread!
To set permissions in Jira Software, you log in as an admin and go to either the permission scheme list in the admin section, or to the project admin and the permissions section.