Pay By Check select a payment type from Register Helper Add On.

rh-payment-type-pay-by-check.php

<?php
/**
 * Creates a custom field for checkout called "Payment Type" which will allow you to specify which payment type was selected for an order.
 * Saves the selection inside the Order > Payment Type.
 * Add this code to your PMPro Customizations Plugin - https://www.paidmembershipspro.com/create-a-plugin-for-pmpro-customizations/
 */
function my_pmprorh_init() {
	//don't break if Register Helper is not loaded
	if(!function_exists( 'pmprorh_add_registration_field' )) {
		return false;
	}
	
	//define the fields
	$fields = array();
	$fields[] = new PMProRH_Field(
		'payment_type',						// input name, will also be used as meta key
		'select',						// type of field
		array(
			'label'  => 'Payment Type',
			'options' => array(				
				''		=> '',			
				'cash'	=> 'Cash',	
				'check'	=> 'Check',	
				'other'	=> 'Other',
			)
		)
	);

	$fields[] = new PMProRH_Field(
		'other_payment_type',						// input name, will also be used as meta key
		'text',						// type of field
		array(
			'label'  => 'Please describe the payment method used',
			'depends' => array(
				array(
					'id' => 'payment_type',
					'value' => 'other' 
				)
			)
		)
	);
	
	//add the fields into a new checkout_boxes are of the checkout page
	foreach($fields as $field)
		pmprorh_add_registration_field(
			'checkout_boxes',				// location on checkout page
			$field						// PMProRH_Field object
		);
	//that's it. see the PMPro Register Helper readme for more information and examples.
}
add_action( 'init', 'my_pmprorh_init' );

function add_payment_type_to_order( $order ) {

	// Bail if payment gateway isn't check.
	if ( 'check' != $order->gateway ) {
		return;
	}

	if ( isset( $_REQUEST['other_payment_type'] ) && ! empty( $_REQUEST['other_payment_type'] ) ) {
		$order->payment_type = esc_attr( $_REQUEST['other_payment_type'] );
	} elseif ( isset( $_REQUEST['payment_type']) && 'other' !== $_REQUEST['payment_type'] ) {
		$order->payment_type = esc_attr( $_REQUEST['payment_type'] );
	}

	$order->saveOrder();
}
add_action( 'pmpro_added_order', 'add_payment_type_to_order' );