Abilash,

You should be able to register custom Api routes like this,

public class EventHandler : IApplicationEventHandler
    {
        public void OnApplicationInitialized(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
        {
            //throw new NotImplementedException();
        }

        public void OnApplicationStarted(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
        {
            //throw new NotImplementedException();
            WebApiConfig.Register(GlobalConfiguration.Configuration);

        }

        public void OnApplicationStarting(UmbracoApplicationBase umbracoApplication, ApplicationContext applicationContext)
        {
            //throw new NotImplementedException();
        }
    }

    public static class WebApiConfig
    {
        public static void Register(HttpConfiguration config)
        {
            config.Routes.MapHttpRoute(
                name:"CustomApi",
                routeTemplate:"api/{controller}/{action}",
                defaults: new {controller = "CustomApiRoute", action = "GetSomeString" }
                );
        }
    }

I just checked it locally and I could hit a sample get action of an UmbracoApiController I wrote like this,

http://localhost:7130/api/customapiroute/getsomestring