Sprinkle fillets with salt and pepper; dredge in flour, shaking off excess.
Heat butter and oil in a large skillet over medium heat; add fillets and cook until halfway done and lightly browned, about 3 minutes; turn and cook until fillets are cooked through about 3 minutes; remove to a platter and keep warm.
To the same pan, add the garlic and cook and stir just to soften, but not brown. Add wine and bring to a simmer, scraping bottom of the pan to remove browned bits; add lemon juice, capers and parsley and briefly heat through. Immediately pour sauce over fillets.
Recipe by A Year at the Table at https://ayearatthetable.com/15-minute-lemony-caper-petrale-sole/