Wash the baby potatoes and cut larger potatoes in half so the pieces are similar in size.
Pat the chicken thighs dry. Season both sides with paprika, Italian seasoning, salt, and black pepper.
Heat the olive oil in a large skillet over medium heat. Add the potatoes cut-side down and cook for about 10–12 minutes, turning occasionally, until golden and nearly tender. Transfer the potatoes to a plate.
Add the chicken thighs to the same skillet and cook for about 5–7 minutes per side, depending on thickness, until golden and the internal temperature reaches 165°F (74°C).
Reduce the heat to low. Add the butter and minced garlic and cook for about 30 seconds, stirring, until fragrant.
Return the potatoes to the skillet and toss gently in the garlic butter around the chicken.
Add the fresh lemon juice and cook everything together for another 1–2 minutes.
Sprinkle with chopped fresh parsley and serve warm with lemon wedges.