Activeadmin: How could I select model records by custom query?

You can override scoped_collection method in your resource controller to fetch resources with custom query.

ActiveAdmin.register Approval do
  index do 
      column :id
      column 'Пользователя', :user
      column 'Заапрувил член клуба', :member
      column :dismiss
      default_actions
  end

  def scoped_collection
    Approval.where(dismiss: false) # this could be   **Approval.dismissed**
  end
end

I've tried to override scoped_collection in the way you wrote. But All the records are still output. Here is the query forming as a result:

where Approval Load (0.2ms)  SELECT "approvals".* FROM "approvals" ORDER BY "approvals"."id" desc LIMIT 30 OFFSET 0

Tnx. Solution:

ActiveAdmin.register Approval do
  index do 
      column :id
      column 'Пользователя', :user
      column 'Заапрувил член клуба', :member
      default_actions
  end
  controller do
    def scoped_collection
      Approval.where(dismiss: false)
    end
  end
end