I tried finding a lot but not getting any option to remote desktop to a App Service hosted on Windows Azure public cloud under Free | Basic plan.
Please suggest how can I remote login to AppService?
Azure App Service is a PaaS offering. There is no Remote Desktop, PowerShell Remoting or SSH.
Depending on what you're looking for you may or may not be able to accomplish it using the Kudu "helper" site (https://sitename.scm.azurewebsites.net).
Wiki:
https://github.com/projectkudu/kudu/wiki/Kudu-console
A nice blog post on Kudu:
https://blogs.msdn.microsoft.com/benjaminperkins/2014/03/24/using-kudu-with-windows-azure-web-sites
Channel9 video from 2013 (Kudu has evolved a lot since then but the basics still apply):
https://channel9.msdn.com/Shows/Azure-Friday/Exploring-the-Super-Secret-Kudu-Debug-Console-with-David-Ebbo
Well, with App Service w/ Containers that's not entirely true anymore since you can now WebSSH into your container from Kudu. Still, an edge case, not something you'd want to do as daily ops.
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https://<app_name>.scm.azurewebsites.net/webssh/host