Buy now button

Hi
I want add a button next to "add to cart button" that allow customer to buy the product directly and move to payment page.  nop version : 4.60.5

Your payment plugin must support this payment method. What plugin are you using?

cashfree plugin

You should contact plugin developer.

okay thank you

If I want buy now button after add to cart button in cart and product detail page , how can I do it?

If you just want to redirect to the cart after adding item to cart, then you will need to customize.
(I'm not aware of any plugin that supports it)

It can probably be done just using HTML/JavaScript.  Likely in this page:
\Views\Product\_AddToCart.cshtml

Note, if you don't want an extra button, and always want to go to the cart, there is a setting:
shoppingcartsettings.displaycartafteraddingproduct

OKay, Thanks

I need some way to let my customers buy and pay directly at the product without "putting" it in the cart. I want my customers to buy only one product at a time. And I really don't need the shipping method selection either.. When the customer sees the product he or she shall click on a "buy" button (not an "add to cart" button) and be redirected directly to the payment/checkout page.. And if they leave the page without paying, I don't want the product to stay "unpaid" waiting for them to pay.. If they leave the page everything shall be restored and normal again.

This will require a bit of customisation.
An order would  still need to be created in a background operation so that the payment and order details can be recorded
Does the customer receive anything for the purchase - I assume as you don't need a shipping address it is not something physical - maybe a digital download or something ?
What payment merchant / type are you going to use Paypal or other ?