@SaiSekhar, MahasivaRavi (Philadelphia) - Thanks for the question and using MS Q&A platform.
Unfortunately, you cannot directly connect on-premise database to Azure Synapse notebooks.
The best way to work with this is to pull the data into Azure Data Lake store, and then run your notebook on the storage account and then write it back to your on-prem servers. Synapse Pipelines should allow this, as well as Azure Data Factory.
If your data store is located inside an on-premises network, an Azure virtual network, or Amazon Virtual Private Cloud, you need to configure a self-hosted integration runtime to connect to it.
For more details, refer to Copy data from a SQL Server database to Azure Blob storage by using the Copy Data tool and Tutorial: How to access on-premises SQL Server from Data Factory Managed VNet using Private Endpoint.
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