Is this JIRA Cloud or Server? If that's Cloud, than you could try https://marketplace.atlassian.com/plugins/com.sngtec.jira.cloud.exporter/cloud/overview - it can export custom fields. It depends on how Test Management stores test cases.
I'll look into it in a bit.
Please see the documentation for Test Management here: https://www.adaptavist.com/doco/display/TMFJC/Exporting+Test+Cases
If you need further assistance, please open a support case: https://productsupport.adaptavist.com/servicedesk/customer/portal/33
Please note, Adaptavist is closed until January 2nd due to the New Year's holiday.
Adaptavist Product Support
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