In a small bowl, combine garlic, capers, and ¼ cup olive oil.
Zest and juice 2 of the lemons and whisk into the caper mixture. Slice remaining lemon and set aside.
Place the mahi mahi fillets in bowl and coat with half of the marinade, refrigerating for 1 hour. Set aside the remaining marinade.
Heat a skillet with the remaining 2 tablespoons of oil over medium-high heat.
Season the fillets with salt and cook on one side for 5 minutes before flipping and cooking on the remaining side for 5 more minutes or until cooked through.
Remove from pan and set aside.
Lower heat, add reserved half of the marinade, lemon slices, and the cold butter.
Swirl until thick sauce forms.
Spoon the sauce over the fish and serve with sliced lemons and parsley.