Open the "IN" in illustrator, or type new letters in that font.
Expand, outline or trace the letters so the characters are editable as paths.
Draw the white shape that is to be clipped out. Make a narrow rectangle and rotate it into place or take the pen tool and draw the shape over the N.
With both the clipping shape and the N selected, open Pathfinder window and click Divide. Ungroup and delete the clipping shape.
This should achieve the desired effect.
I see the graphic breakup you got. Not sure what caused it but I have suggestions to fix it.
Before deleting the white clip ungroup everything and look at the shapes. Is the original white rectangle there, and also the jaggy parallelograms? Select every little shape that's supposed to be part of the N, and the rest of the N and hit Unite in the pathfinder window. This will combine them back together.
If the missing bits are not individual pieces, before you divide or clip anything select the "IN", remove stroke, expand and unite. Then do the clipping with the white rectangle. This should make a clean clip.