Either buy a new smaller Mezuzah, or put this case in your breakfront for display and purchase a new case the correct size. Folding a Mezuzah and inserting it sideways is not the solution. A Kosher Mezuzah needs to be rolled upright from left to right like a scroll, so that if we were to open it from the right we would be able to read the text.
In addition the fold in this particular Mezuzah was so sharply creased that it broke all the letters on the crease and the Mezuzah was no longer Kosher.
Lesson: Have a certified Sofer insert your Mezuzos in your case for you, to ensure that it will be done correctly.