api\regions_controller.rb

class Api::RegionsController < ApplicationController
  def provinces
    prompt = [
        {
            id: "",
            name: core_model_lang("province")
        }
    ]
    @provinces = prompt + Province.all
    render json: @provinces.to_json(only: [:id, :name])
  end

  def regency_id
    @regency_id = Regency.where(province_id: params[:id])
    render :regency_id, layout: false
  end

  def district_id
    @district_id = District.where(regency_id: params[:id])
    render :district_id, layout: false
  end

  def village_id
    @village_id = Village.where(district_id: params[:id])
    render :village_id, layout: false
  end
end

app.coffee

if $('#province_id') and $('#province_id').is(':empty')
  $.ajax
    type: 'GET'
    url: '/api/regions/provinces'
    success: (data) ->
      $.each data, (string, value) ->
        $('#province_id').append '<option value="' + value.id + '">' + value.name + '</option>'

$('#province_id').change ->
  province_id = $('#province_id').val()
  $.ajax
    type: 'POST'
    url: '/api/regions/regency/' + province_id
    success: (data) ->
      $('#regency_id').html data
  $('#regency_id').val ''

$('#regency_id').change ->
  regency_id = $('#regency_id').val()
  $.ajax
    type: 'POST'
    url: '/api/regions/district/' + regency_id
    success: (data) ->
      $('#district_id').html data
  $('#district_id').val ''

$('#district_id').change ->
  district_id = $('#district_id').val()
  $.ajax
    type: 'POST'
    url: '/api/regions/village/' + district_id
    success: (data) ->
      $('#village_id').html data
  $('#village_id').val ''

routes.rb

namespace :api do
  get "regions/provinces", to: "regions#provinces", format: :json
  post "regions/regency/:id", to: "regions#regency_id", format: "html"
  post "regions/district/:id", to: "regions#district_id", format: "html"
  post "regions/village/:id", to: "regions#village_id", format: "html"
end