Preheat the oven to 400°F (200°C).
In a medium bowl, toss the halved baby potatoes with 3 tablespoons olive oil, 3 cloves minced garlic, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until evenly coated.
Spread the potatoes on a baking sheet in a single layer and roast in the oven for 20 minutes.
Meanwhile, in a small bowl, combine 2 tablespoons olive oil, lemon zest, lemon juice, 2 cloves minced garlic, dried thyme, dried parsley, 1/2 teaspoon salt, and 1/4 teaspoon black pepper to make the marinade.
Place the white fish fillets in a shallow baking dish and pour the marinade over them, turning to coat evenly. Let them marinate while the potatoes roast.
After the potatoes have roasted for 20 minutes, remove the baking sheet from the oven and gently push the potatoes to one side.
Place the marinated fish fillets on the other side of the baking sheet and return to the oven. Bake for 10 to 12 minutes, or until the fish is opaque and flakes easily with a fork and the potatoes are tender and golden.
While the fish and potatoes finish baking, bring a medium pot of salted water to a boil.
Add the green beans and cook for 3 to 4 minutes until tender-crisp.
Drain the green beans and return them to the pot. Stir in 1 tablespoon unsalted butter and 1/4 teaspoon salt until the butter melts and the beans are coated.
Serve the baked white fish fillets with roasted garlic potatoes and steamed green beans on the side.