You can use whatever oil you would normally fry in, but a typical oil to use is canola or vegetable oil. You want to use a neutral-flavored oil that won't add anything to the beignets. You should avoid oils like olive oil or butter, as they impart a strong flavor and may not give you the results you want. Canola oil is often used for frying because it has a high smoke point and doesn't impart much flavor to foods. Another option some people use is peanut oil, but it is my least favorite of the oils due to potential allergies as well as flavors.