Only use triangles with the subsurf modifier if they are on a planar surface. For curved faces just use quad faces, preferably evenly sized and close to a square shape with a topology that follows the surface shape of the object
Ok sorry i feel like a total noob asking this but ummm is there a specific way you got your mesh like that, cuz i just kinda manualy did this with extrusions and scaling and ended up with a kinda…bad result