The Shopify API doesn't have a "Paid At" field but a workaround is to look at the "Transaction Dates" data.

In EZ Exporter, set the "Payment status" filter first to "Paid." Then in the Fields section, select the field called transactions.last_successful_transaction.created_at.

The logic here is if the order status is in "Paid" status, then the last successful transaction date would be the date the order was paid.