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Path variables should be part of your API URL. So, in Azure Synapse Copy activity, you need to use dataset which is REST connector type and in URL itself you need to include the path variable value.
Please check below screenshots:
Request from Postman :
To create same request from Synapse, create a linked service which is REST type and create a dataset REST type use this linked service and use that dataset in copy activity.
Hope this helps. Please let me know if any further queries.
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