Can I change the sort order of my Shopify payment methods?

The display of the payment method in the Shopify Checkout is generally not controlled by us. This is done by the Shopify Checkout. Therefore if you a standard Shopify User (Basic - Advanced) you can not influence this. 

However, if you are a Shopify Plus user you have access to the checkout.liquid and you are able to change the sort order of the payment methods in the checkout.