Apologies for the delay on this. To better assist you on this, could you please provide more details on your app and the requirement?
On Azure App Service WebApp (on the tag posted here)- ports other than 80 and 443 are ignored.
If your requirement fits you may look at Azure Container Instances as an option.
Azure offers a number of ways to host your application code. The term compute refers to the hosting model for the computing resources that your application runs on. The following flowchart will help you to choose a compute service for your application.
I suggest you take a look at the criteria and flow chart (Decision tree for Azure compute services), weigh the platform strengths based on your organizational requirement and then chose the best platform.
As a side note, If you’re looking to deploy WebJobs (to Run background tasks). By uploading an executable or script. You can run background tasks in the Azure App Service.
However, webJobs is a feature of Azure App Service that enables you to run a program or script in the same instance as a WebApp.