I am using Action Link Template to redirect my user in sf1. It is working fine in SF1 Simulator and one/one.app. But in the SF1 app it redirect user to Desktop website. is there any way we can move the user into SF1 from here
Action links are a developer feature that can be used to add more complex functionality into Chatter Feed posts in the form of an interactive button. These can be used to take a user to a Web page, initiate a file download, or invoke an API call to Salesforce or an external server.
Currently the Action Link and Action Link Template features are not supported in the Salesforce1 hybrid (downloadable) applications on iOS and Android devices.
Users may see Feed posts where the Action Link button is not displayed or the Action Link does not behave as expected. For example, when navigating to another Visualforce page the navigation does not register that the user is in Salesforce1 and tries to display the full-site version of the page.
Resolution: These features are fully supported for the mobile browser version of Salesforce1 on supported browsers.
It sounds as though the page you're redirecting to isn't enabled for SF1 mobile. You should also add a tab for the page you're redirecting to for use with SF1. I highly recommend that you visit Trailhead and go through the Visualforce Mobile Module.
I found a blog post by @AndrewFawcett titled Using Action Link Templates to Declaratively call API’s that may be helpful to you in resolving your issue. In it, I noticed this image that relates to the Group Template Edit Overflow Action Edit Options:
Andrew does a great job of explaining how Action Link Templates work and that they also need to have a Group Action Template to encapsulate them as well. He goes into great detail and has some diagnostic tips for use in the Developer Console. I recommend you read his article to see if there's something in your template may not have been configured in the manner necessary to function as expected.