GetOrdersByPaymentMethod

extension_attributes.xml

<?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="Magento\Sales\Api\Data\OrderInterface">
        <attribute code="payment_method_code" type="string">
            <join reference_table="sales_order_payment" reference_field="parent_id" join_on_field="entity_id">
                <field>method</field>
            </join>
        </attribute>
    </extension_attributes>
</config>

Orders.php

<?php

declare(strict_types=1);

namespace MageVision\Blog72\Block;

use Magento\Framework\Api\FilterBuilder;
use Magento\Framework\Api\SearchCriteriaBuilder;
use Magento\Framework\View\Element\Template;
use Magento\Framework\View\Element\Template\Context;
use Magento\OfflinePayments\Model\Checkmo;
use Magento\Sales\Api\OrderRepositoryInterface;

class Orders extends Template
{
    private SearchCriteriaBuilder $searchCriteriaBuilder;

    private FilterBuilder $filterBuilder;

    private OrderRepositoryInterface $orderRepository;

    /**
     * @param Context $context
     * @param SearchCriteriaBuilder $searchCriteriaBuilder
     * @param FilterBuilder $filterBuilder
     * @param OrderRepositoryInterface $orderRepository
     * @param array $data
     */
    public function __construct(
        Context $context,
        SearchCriteriaBuilder $searchCriteriaBuilder,
        FilterBuilder $filterBuilder,
        OrderRepositoryInterface $orderRepository,
        array $data = []
    ) {
        parent::__construct($context, $data);
        $this->searchCriteriaBuilder = $searchCriteriaBuilder;
        $this->filterBuilder = $filterBuilder;
        $this->orderRepository = $orderRepository;
    }

    /**
     * Get orders purchased with checkmo payment method
     *
     * @return void
     */
    public function getOrderByPaymentMethod()
    {
        $searchCriteria = $this->searchCriteriaBuilder
            ->addFilters(
                [
                    $this->filterBuilder->setField('extension_attribute_payment_method_code.method')->setValue(Checkmo::PAYMENT_METHOD_CHECKMO_CODE)->create()
                ]
            )
            ->create();

        $orders = $this->orderRepository->getList($searchCriteria);

        foreach ($orders->getItems() as $order) {
            //Your logic
        }
    }
}