Adjust oven rack to center position and preheat oven to 350°F (175°C). Season chicken generously with salt and pepper. Heat oil in a sauté pan or Dutch oven over medium-high heat until shimmering. Add chicken, skin side down, and cook, without moving, until well browned and crisp, about 8 minutes. Flip chicken and brown lightly on second side, about 3 minutes. Transfer chicken to a large plate and set aside.

Add sausage to the skillet without draining it and cook until well browned on first side, about 1 ½ minutes. Flip sausage and cook on second side until browned, about 1 ½ minutes longer. Remove pan from heat, transfer sausage to a cutting board, and cut each link into 3 to 4 slices.

Return pan to heat, add onion and bell pepper, and cook, stirring and scraping up browned bits with a wooden spoon, until softened and starting to brown, about 4 minutes. Add sage and garlic, stir to combine, and cook until fragrant, about 1 minute.

Add pickled cherry peppers and their liquid, stirring and scraping up browned bits from bottom of pan. Add wine and cook until liquid is reduced by half, about 2 minutes. Add chicken stock and sugar, and stir to combine. Return sausage to pan, toss to combine, then return chicken pieces to pan skin side up, nestling them among sauce, vegetables, and sausage.

Transfer to oven and cook until chicken is crisp and tender, about 30 minutes. Serve immediately, spooning sauce, vegetables, and sausage around chicken pieces.