According to Wikipedia, Shadowhunters is meant to adapt all the books and seems to have started from the first book.
In 2010, Screen Gems announced that they were going
into production on the film adaptation of City of Bones, the first
book in The Mortal Instruments series, with hopes of starting a
successful film franchise. Production on a film adaptation of the
second book, City of Ashes, was due to start in September 2013, but
was delayed to 2014, and eventually cancelled, after the first film
failed to recoup its budget.
On October 12, 2014, at Mipcom, Constantin confirmed that The Mortal
Instruments will return as a television series with Ed Decter as
showrunner. Constantin Film and TV head Martin Moszkowicz told The
Hollywood Reporter that, "It actually makes sense to do [the novels]
as a TV series. There was so much from the book that we had to leave
out of the Mortal Instruments film. In the series we'll be able to go
deeper and explore this world in greater detail and depth."
The producers hope to adapt the entire book series if the TV
adaptation proves successful. In February 2015, book series author
Cassandra Clare announced via Twitter that the television series would
be called Shadowhunters rather than The Mortal Instruments. In
March 2015, ABC Family picked up Shadowhunters straight-to-series.
The series was renewed for a second season in March 2016, consisting
of 20 episodes, which premiered on January 2, 2017. In
April 2017, it was announced that the series was renewed for a third
season of 20 episodes. The first half of ten episodes is set to
premiere on March 20, 2018, while the second half will air from
In August 2016, soon before filming on the second season was to begin,
showrunner Ed Decter exited the series over "creative
differences". Todd Slavkin and Darren Swimmer, who were former
showrunners on Smallville, were announced as Decter's replacements in
August 2016. https://en.wikipedia.org/wiki/Shadowhunters
However, an older Bustle article about trying to figure out when or what book the TV series' second season takes place, states that there are A LOT of changes between the source material and the TV adaptation, but does explain that the first season basically covered the first two books and something that happens in the third. (I Do not know what the second season covered, since I have not watched much of the show or have ever read the books, but at least the following gives an idea).
Note: Season Three is set to premiere March 20, 2018
Shadowhunters as an adaptation of the Mortal Instruments books has made a lot of changes from the source material, which isn't
necessarily surprising or upsetting. Different mediums tell stories at
different paces and with different emphases, and so characters and
moments have been moved around in the Freeform adaptation. Which
Mortal Instruments novel is Shadowhunters Season 2 based on? It's not
exactly easy to pin down.
The first season started at the very beginning with the very first book City of Bones — a very good place to start. That means,
however, that much of the season bore a resemblance to the Mortal
Instruments movie. In a smart move by Freeform, the series quickly set
itself apart by delving into other books from Cassandra Clare's
fandom. The show also introduced characters like Camille, who was
mentioned in City of Glass but first appeared in the ancillary novel
Clockwork Angel. Clare has created an expansive mythology that the
Freeform series is really taking advantage of in a smart way.
In only thirteen episodes, Season 1 also covered much of City of Ashes, the second book in the series. Plus, Season 1 ended with
Jocelyn waking up, which happens in the third book, City of Glass,
and that gives fans a good landmark as to the timeline, even with the
changes that the Freeform series has made. Vampire Simon, anyone?