Butter makes everything better, but the milk solids (which will burn) within it mean it's not the best candidate for high temperature cooking. Clarified butter (also known as "ghee"), on the other hand, is lacking such solids, making it a super delicious choice for frying.
If you've never clarified butter before, Daniel Gritzer of Serious Eats can walk you through the process here, but it's basically a matter of boiling butter until the foaming and bubbling subsides, and straining out the solids that fall to the bottom. Once you've done that, your butter is now ready to replace boring, less flavorful cooking oils. Serious Eats has a great method for cooking chicken cutlets this way (linked below) but I'm thinking fried green tomatoes, hash browns, and onion rings would all benefit from the this rich and tasty cooking fat.