Hi,
I assume that this APIs is outside of Microsoft Azure platform if that the case you need to withelist the public Ips of Azure managed services (In this case Synapse).
https://learn.microsoft.com/en-us/azure/synapse-analytics/security/gateway-ip-addresses
To update the ipaddresses automatically you can get the lastest list from :
https://www.microsoft.com/en-us/download/details.aspx?id=56519
On the other hand If these APIs are within Azure services ,you can use a network service like private endpoint or peering to make the communication internally.
Cheers,
Luis Arias
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