Auto Deploy after push to git
You can achieve this using Git and Jenkins job. Create a Jenkins Job to deploy your code to server and Setup Git webhook to Call Jenkins job. 

Check this link: https://www.serverkaka.com/2019/02/configure-github-webhook-in-jenkins-job-pipeline.html


  OR



Create an empty Git repo on the server
Write a Git Hook to deploy the code
Deploy from the local computer


Check this link: https://medium.com/@francoisromain/vps-deploy-with-git-fea605f1303b