Researchers want the public to test themselves: https://yourmist.streamlit.app/. Selecting true or false against 20 headlines gives the user a set of scores and a “resilience” ranking that compares them to the wider U.S. population. It takes less than two minutes to complete.
The paper
Edit: the article might be misrepresenting the study and its findings, so it’s worth checking the paper itself. (See @realChem 's comment in the thread).
I suspect that where you select on the extremely liberal to extremely conservative spectrum might have a correlation to which fake news titles you fall for. What sounds like obvious propaganda to you may sound like any news article that some may see from a more sensationalist less reliable news source, especially to those predisposed to conspiracy theories.
Of course, there are a few people out there who won’t even identify headlines like “Ebola Virus ‘Caused by US Nuclear Weapons Testing’, New Study Says”, “Government Officials Have Illegally Manipulated the Weather to Cause Devastating Storms”, and “Left-Wing Extremism Causes ‘More Damage’ to World Than Terrorism, Says UN Report” as fabricated even when filling out a survey about fake news. But at that point they’re not testing susceptibility to fake news, they’re testing whether you’ve already fallen down the conspiracy rabbit hole and hit your head hard enough on the way down to render you incapable of even slight scepticism.
A better study would be, in my opinion, to present screen shots of actual content from social media (Facebook, Reddit, Twitter, wherever), and have users rank it on a scale from 1 to 7 how much they trust it (not at al <----> completely). That way you can observe sources, content, how many “likes” a post has, and more dimensions that are more valid indicators of how people might (mis)judge content as being true or false.