This question has been answered by m.engel. See the first response.
[[!Peoples? &where=`{"Profile.id:=":30}`]]$query = '"showprofile":"on"';
$c->where(array('Profile.extended:LIKE' => '%'.$query.'%'));[[!Peoples? &where=`{"Profile.extended:LIKE":"%\"showprofile\":\"on\"%"}`]]It should work as you did
[[!Peoples? &where=`{"Profile.extended:LIKE":"%\"showprofile\":\"on\"%"}`]]
is probably right, cant test it now