JSONP and unsafe scripts

I have decided to revisit my random quote generator project after finally completing the weather app correctly. I am almost finished with the Wikipedia Viewer (it’s just down to aesthetics). Before these projects, I had no clue what an API was or how to use one, so I hardcoded a bunch of quotes and authors in an array. I decided I wanted to have cleaner code by using a quote API, but none are on https that I have found, leaving me to use jsonp. Finally, I got that working, but it is impossible to have anything happen on my cell phone or iPad when I click the button. I thought the point to using jsonp was to fix the cross-origin header problem, but what good is it if you can’t do anything because of unsafe scripts?

How do I fix this problem?