We have a person who is 'Batman' to triage production issues. Generally they'll pick up smaller sprint tasks. It rotates every week. It's still stuff from the team so they aren't doing stuff unknown (or if they are, it's likely they'll work on it soon).
The aim is generally not to provide a perfect fix but an MVP fix and raise tickets in the queue for regular planning.
It rotates round every week or so.
My company's not very devops so it's not on-call, but it's 'point of contact'.