The best replacement for normal force is frictional force.

The best alternatives to normal force are rated as following:
★★★★★  frictional force
★★★★★  gravitational force
★★★★  shear force
★★★★  net force
★★★  friction
★★★  contact force
★★  applied force
★  kinetic friction
★  static friction
  apparent weight

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normal force
frictional force
gravitational force