Basic and Windows Without Impersonation Authentication in Personal Gateway

ashish_pradhan,

• Windows Authentication
  When a user connects through a Windows user account, SQL Server validates the account name and password using the Windows principal token in the operating system.
• SQL Server Authentication
  When using SQL Server Authentication, logins are created in SQL Server that are not based on Windows user accounts. Both the user name and the password are created by using SQL Server and stored in SQL Server.

Reference
https://docs.microsoft.com/en-us/sql/relational-databases/security/choose-an-authentication-mode

The gateway needs to have access to the data source. If your personal machine cannot connect to the data source, you may want to consider installing an On-premises Data Gateway on a machine that does have access to the data source.

So in your scenario, the issue could casued by your local machine do not have access to your SQL Server machine. Please install on-premisses data gateway on your SQL Server machine and use windows authentication on your data gateway.

Regards,

Charlie Liao