// appcode[Vendor][Module]BlockAdminhtmlPointEditForm.php

$balloonFieldset->addField(
            'payment_types',
            'checkboxes',
            [
                'label' => __('Payment Types'),
                'name' => 'payment_types',
                'values' => [
                    ['value' => '2','label' => 'Card'],
                    ['value' => '3','label' => 'Cash'],
                    ['value' => '4','label' => 'Prepaid'],
                ],
            ]
        );

/**
     * Set payment_types
     *
     * @param array $paymentTypes
     * @return RoundropFrontPageApiDataPointInterface
     */
    public function setPaymentTypes($paymentTypes)
    {
        $stringTypes = implode(', ', $paymentTypes);

        return $this->setData(self::PAYMENT_TYPES, $stringTypes);
    }

    /**
     * Get payment types
     *
     * @return string|null
     */
    public function getPaymentTypes()
    {
        return explode(', ', $this->getData(self::PAYMENT_TYPES));
    }

'name' => 'payment_types',

'name' => 'payment_types[]',