Ted here from Shopify, thanks for reaching out to us.
Normally if an order can't be seen in the Shopify admin but it can be seen in your payment gateway account, it means that the customer left the payment screen after they paid and did not wait for the order confirmation screen. For example, when they confirmed the payment on Paypal's website, they were not redirected back the the "Thank you" page on Shopify's checkout.
You would have two options here if you can't see the order in your admin. The first option would be to refund the orders in full and let the customers know there was an error with the order and it had to be cancelled/refunded. You could then encourage them to purchase from your store again and even offer a small discount. The second option here would be to contact them and ask if they received any order confirmation email from your store (other than Paypal's confirmation email). If not, you could just let them know that the order didn't come through fully and you could replicate the order with them using the Draft Order option in your admin as shown here. Bear in mind you will need the order info, quantity, shipping address and phone number. After that information has been listed in the draft order, you could then mark it as paid manually since you've already received the payment and then continue with its fulfilment.
Please me know how this goes and if there is anything else I can help you with, I'm happy to help!