<?php
class Assignment extends Model {
    ...

    public function product()
    {
        return $this->belongsTo('App\Models\Product', 'global_products_id', 'global_products_id');
    }

...


class Product extends Model
{
    ...

    public function assignment()
    {
        return $this->hasMany('App\Models\Assignment', 'global_products_id', 'global_products_id');
    }

...


$query = Assignment::where('prefix', $prefix)->with('product')->get();


$result = [
    {
        "id": 1,
        "global_products_id": 7,
        "product": null                    <==== why?
    },
    {
        "id": 2,
        "global_products_id": 30,
        "product": {
            "id": 30,
            "name": "---------",
            ...
        }
    },
    ...
];