How deploy source code as an application in a linux virtual machine on Azure using Jenkins?

Your Jenkins is already configured in your local windows-10 but you show us a link to Create a Jenkins server on an Azure Linux VM from the Azure portal. I think you are a little confused.

My advice related to a basic infrastructure on your Azure is:

• Have a Jenkins in a linux machine on azure
• According to your programming language, configure another linux machine on azure (if you are not using .net).
• Use github, gitlab or bitbucket as repository to your source code.

From your windows 10, you just need to push changes using git.

My advice related to a basic integration between Jenkins, source code repository and your application server, could be:

https://stackoverflow.com/a/53835514/3957754

Nowadays the previous flow or integration is common. Of course, exist more complex approaches like : kubernetes, ansible, artifact repository, jenkinsX, etc or saas providers with minimal configurations like : jelastic, heroku, openshift,etc

From your info and log, I see that you've configured master Jenkins on your Windows computer, but trying to run the job remotely on Ubuntu agent:

Building remotely on testadminjenkinsazure115f10 (ubuntu) in workspace /home/Jenkinsadmin/workspace/mySampleApp

So, you need to install Git on your Ubuntu VM. As JRichardsz already said, from Windows you just need to push changes to Git server.