<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <type name="MagentoSalesApiOrderRepositoryInterface">
        <plugin name="save_custom" type="MyProjectPluginOrderSave"/>
        <plugin name="get_custom" type="MyProjectPluginOrderGet"/>
    </type>
</config>

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Api/etc/extension_attributes.xsd">
    <extension_attributes for="MagentoSalesApiDataOrderInterface">
        <attribute code="custom" type="MyProjectApiDataCustomAttributeInterface" />
    </extension_attributes>
</config>

<?php

namespace MyProjectApiData;

interface CustomInterface
{
    const NAME = 'custom';

    /**
     * Return value.
     *
     * @return string|null
     */
    public function getValue();

    /**
     * Set value.
     *
     * @param string|null $value
     * @return $this
     */
    public function setValue($value);
}

<?php

// ... some code

class OrderGet
{

    // constructor and other code...

    public function afterGet(
        OrderRepositoryInterface $subject,
        OrderInterface $resultOrder
    ) {
        $resultOrder = $this->getCustomAttribute($resultOrder);

        return $resultOrder;
    }


    private function getCustomAttribute(OrderInterface $order)
    {
        try {
            $somwhere = $this->someFactory->create();
            $somwhere->load($order->getIncrementId(), 'order_id');

            if (!$somwhere->getId()) {
                throw new NoSuchEntityException('No custom entity found for id' . $order->getIncrementId());
            }

            // This will get the custom value from the database
            $customAttributeValue = $this->someHelper->getCustomConfig($somwhere->getData('some_id'));

        } catch (NoSuchEntityException $e) {
            return $order;
        }

        $extensionAttributes = $order->getExtensionAttributes();
        $orderExtension = $extensionAttributes ? $extensionAttributes : $this->orderExtensionFactory->create();
        $customAttribute = $this->customAttributeFactory->create();
        $customAttribute->setValue($customAttributeValue);
        $orderExtension->setCustomAttribute($customAttribute);
        $order->setExtensionAttributes($orderExtension);

        return $order;
    }
}