Open additional ports on Azure Web App
Solution 1:
No, you cannot. Only ports 80 and 443 are open.
Check this answer on Server Fault: https://serverfault.com/a/751548/394375.
If you need that control, you can use Cloud Services or Virtual Machines.
Solution 2:
While Azure Web App cannot expose ports 8080 and 444, you could use Application Gateway to export those ports and route incoming traffic on 8080 and 444 to ports 80 or 443 on a Web App.
Solution 3:
In case you consider containerizing and deploying your app:
By default, App Service assumes your custom container is listening on port 80. If your container listens to a different port, set the WEBSITES_PORT app setting in your App Service app. You can set it via the Cloud Shell. In Bash:
az webapp config appsettings set --resource-group <group-name> --name <app-name> --settings WEBSITES_PORT=8000
App Service currently allows your container to expose only one port for HTTP requests.
Source: https://docs.microsoft.com/en-us/azure/app-service/configure-custom-container?pivots=container-linux#configure-port-number
Solution 4:
You can configure the app to use other ports. Based on the answer on Github,
the automatic port detection detects the port (port 80 is the default), we will attempt to detect which port to bind to your container, but you can also use the WEBSITES_PORT app setting and configure it with a value for the port you want to bind to your container. However, the webserver in your custom image may use a port other than 80. You tell Azure about the port that your custom container uses by using the WEBSITES_PORT app setting. In this case, yes you will have to change the App Setting configuration from the Portal.