As the official documentation doesn’t specify how exactly to create a custom
validation class.

1. Create custom validator class

You can create in any where as you like. For my example, I will create in
app/Libraries/CustomValidator.php

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<?php namespace App\Libraries;

class CustomValidator
{
    /**
     * custom_rule:$param1,$param2,...
     * 
     * @param mixed $attribute 
     * @param mixed $value 
     * @param mixed $parameters 
     * @return bool
     */
    public function validateYourCustomRule($attribute, $value, $parameters)
    {
        // validate
        return false;
    }
}

2. Update to provider

Edit the file app/Providers/AppServiceProvider.php

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<?php namespace App\Providers;

use Illuminate\Support\ServiceProvider;

class AppServiceProvider extends ServiceProvider
{
    /**
     * Bootstrap any application services.
     *
     * @return void
     */
    public function boot()
    {
        \Validator::extend('custom_rule', 'App\Libraries\CustomValidator@validateYourCustomRule');
    }

    /**
     * Register any application services.
     *
     * @return void
     */
    public function register()
    {
        //
    }
}

3. Add the error message to language file

Edit resources/lang/en/validation.php and add this

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'custom_rule' => 'The :attribute has custom error.',

Test it

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<?php
...
$rules = [
    'attr' => 'custom_rule:param1,param2',
];

References: