Example of API with ransack search and kaminari paginate.

cities_controller.rb

class Api::CitiesController < Api::ApplicationController
  respond_to :json
  
  ##
  # Get list of cities.
  #
  # @note Default per_page option is 10.
  #
  # @overload index(q)
  #   @param [Hash] q Ransack search paramsh
  #
  # @see https://github.com/ernie/ransack/wiki/Basic-Searching
  def index
    q_param = params[:q]
    page = params[:page]
    per_page = params[:per_page]

    @q = City.ransack q_param
    @cities = @q.result.page(page).per(per_page)
  end

  ##
  # Get city by ID
  #
  def show
    @city = City.find_by_sub_domain params[:id]
  end
end

city.rb

class City < ActiveRecord::Base
  attr_accessible :name, :location

  validates :name, :presence => true, :uniqueness => true
end

Gemfile

gem 'kaminari'
gem 'ransack'

kaminari_config.rb

# In config/initializers
Kaminari.configure do |config|
  config.default_per_page = 10
  config.window = 2
  config.param_name = 'q[page]'
end