Step 1: The eponym Killian points straight to nasal septal surgery. The cut is curvilinear and placed a few millimetres above the caudal edge of the septal cartilage on the concave side of the deviation.
Step 2: This approach belongs to septoplasty, where the surgeon raises a mucoperichondrial flap, separates the septal cartilage from the vomer and ethmoid plate, and reshapes only the deviated parts while keeping the supporting framework intact.
Step 3: Submucous resection is associated with a transfixion or Freer's incision and aims to remove cartilage and bone rather than conserve it, so it does not fit the Killian eponym as well.
Step 4: Proof puncture targets the maxillary sinus through the inferior meatus and a modified radical mastoidectomy is an ear procedure done via a postaural route; neither involves a septal incision. The correct match is septoplasty.
\[\boxed{\text{Septoplasty}}\]