You'd like servant:

http://haskell-servant.github.io/tutorial/#tutorial

(Author here) There is a set of exercises that come with the slides at https://github.com/serras/lambdaconf-2015-web In particular, they introduce the Aeson library for both producing and consuming JSON.

You should check out PostgREST, a tool to expose Postres tables through a JSON APIs: https://github.com/begriffs/postgrest

I believe the HTML templating stuff is pretty optional in all the major Haskell web platforms. I know in Yesod it is trivial to serve JSON rather than HTML from an end-point, and pretty easy to serve multiple representations of the same resource.

"aeson" is the go-to library for producing and parsing JSON in Haskell.

thoughtbot's carnival is a good example of a JSON API written with Yesod: https://github.com/thoughtbot/carnival