How can I make my own custom JSON Request from another API?

I am new to web development but not to programming as a whole. I am looking to make an app that gets a JSON request from an API. However, I want to make this request on a website and then get the information from the website instead with my own custom JSON (or the exact same JSON).

The reason I would like to do this is because I want the website server to make the request to the real API every 10 minutes. That way my app requests my websites JSON instead. I may be explaining this bad but I'll make a flow chart to below to help explain it better.

Real API <== Website Server (Requests real API every 10 minutes) <== My App (Requests from Website server)

I just want some pointers or advice to how I should go about doing this.