is there any way to publish my API in azure mobile service API instead of using its own. I want just to know it, because assume I have a backup server in amazon and as you know I don't have access to azure sdk in there and it means technically I cant use the API anywhere outside the azure.
Azure mobile services is actually based on the .Net web api in their C# flavor and on node.js on the Javascript side. You could surely write an API using those technology and have the same behavior. You will gain the fact of being more portable, however you will lose some of the preconfigured stuff from Mobile services.
If you are using .NET, please check this to see how to build a Web api! http://www.asp.net/web-api.
If you are using Javascript, here is where you should start : https://nodejs.org/
Both tech are quite easy to learn and super powerfull, have fun! When your API is built, you could just publish them as an azure Web APP (http://azure.microsoft.com/en-us/services/app-service/web/) or an Azure API (https://azure.microsoft.com/en-us/services/app-service/api/) instead of the mobile App
Hope it helps, if you have more questions, please ask!