Ionic Product is basically the equilibrium constant for the reversible reaction

H₂O -> H⁺ + OH^-

As the equilibrium constant  for any reaction is constant at a given temperature, the Ionic product also remains the same, regardless of the acidity or basicity of the medium.

If you're asking how,

The extra H+ in acidic medium will react with some OH- from water to such an extent that the Ionic product is 10^ -14