A tricky one, especially as many people struggle with apostrophes these days – many of them were not have been taught them correctly at school.
The answer is the subject of a long-running debate! See this article
In fact, both are correct. Which is why you see both styles used.
However, you shouldn’t expect to see both styles used in the same publication or website.
The fact there are two ways of expressing the term means a publisher should use a style guide to choose between one or the other, in order to to achieve consistency.
Students on our online proofreading course follow the Guardian style guide, which prefers St. James’s.
See our proofreading course