This can be accomplished in a few simple steps

1. Make a Trigger for the search
2. Fetch the data from an API & Load the data into the form state

If you just want to see the entire code example you can skip to this section

#Explanation

Lets see how this can be accomplished with an example:

#Search trigger

We are going to start with this very simple form schema. Our goal is to automatically fill the country_region & country_subregion, based on country_name

protected function getFormSchema(): array
{
    return [
        TextInput::make('country_name'),
        TextInput::make('country_region'),
        TextInput::make('country_subregion'),
    ];
}

Our search trigger will be a ->suffixAction() on the TextInput

use Filament\Forms\Components\Actions\Action;
//...
TextInput::make('country_name')
    ->suffixAction(fn ($state, Closure $set) => Action::make('search-action')
        ->icon('heroicon-o-search')
        ->action(function () use ($state, $set) {
            //Notice how `$state` & `$set` are injected. These will be used later on
            //We will leave this blank for now
        })
    ),

#Fetch & load data

Lets just focus on the action.

Action::make('search-action')
    ->icon('heroicon-o-search')
    ->action(function () use ($state, $set) {
        //$state is state of this(country_name) field, i.e. the search term
 
        //Always a good idea to check using blank() whenever using a field state
        if (blank($state))
        {
            //notify the user that they must enter a search term
            Filament::notify('danger', 'Please enter a country name');
            return;
        }
 
        //make the request to the api
        try {
            //Not going into too much detail here,
            //because how the data is fetched is up to you and not relevant to filament
            $countryData = Http::baseUrl('https://restcountries.com/v3.1/name')
                ->get($this->data['country_name'], ['fields' => 'region,subregion'])
                ->throw()
                ->json('0');
        } catch (RequestException $e) {
            //notify the user that the api request failed
            Filament::notify('danger', 'Unable to find the country');
            return;
        }
 
        //using $set we can set the value of another field
        $set('country_region', $countryData['region'] ?? null);
        $set('country_subregion', $countryData['subregion'] ?? null);
    })

#Entire Example Code

protected function getFormSchema(): array
{
    return [
        TextInput::make('country_name')
            ->suffixAction(fn ($state, Closure $set) =>
                Action::make('search-action')
                    ->icon('heroicon-o-search')
                    ->action(function () use ($state, $set) {
                        if (blank($state))
                        {
                            Filament::notify('danger', 'Please enter a country name');
                            return;
                        }
 
                        try {
                            $countryData = Http::baseUrl('https://restcountries.com/v3.1/name')
                                ->get($this->data['country_name'], ['fields' => 'region,subregion'])
                                ->throw()
                                ->json('0');
                        } catch (RequestException $e) {
                            Filament::notify('danger', 'Unable to find the country');
                            return;
                        }
 
                        $set('country_region', $countryData['region'] ?? null);
                        $set('country_subregion', $countryData['subregion'] ?? null);
                    })
                ),
        TextInput::make('country_region'),
        TextInput::make('country_subregion'),
    ];
}