How does the use of fertilizer affect the nitrogen cycle

It don’t

Explanation:
We might think that adding specific nitrogen compounds to agriculture would affect the nitrogen cycle. But, it really is just a part of a much larger system as shown by the included graphics.
As a "cycle" the nitrogen is continuously removed from the atmosphere and ground sources, used by plants for growth, and then fixed, immobilized or leached or removed back to the soil or atmosphere.