> Add Route with parameter in api.php file Laravel framework

Route::get('test', [
    'as' => 'test',
    'uses' => 'Front\TestController@extra'
])->name('test');

> Make simple API using Jquery Ajax

$("#<Your Element ID>").on('change keydown paste input', function(event) {
    $.ajax({
        url: '/api/test/?q='+event.target.value,
        headers: {
            'X-CSRF-TOKEN': $('meta[name="csrf-token"]').attr('content')
        },
        method: 'GET',
        dataType: 'json',
        beforeSend: function() {
        }
    }).done(function (data) {
       console.log(data);
    });
});

> Here is TestController.php

public function extra(Request $request) {
    \Log::info($request->query('q'));
}