Depending on its size, it may disrupt the straight edge of the vocal fold. If it does this, the voice becomes hoarse. More hoarseness is noted if the cyst contacts the other vocal fold, causing it to swell. Then both vocal folds have a bump on the edge and the voice can be severely hoarse.
A cyst appears as a round object within the vocal fold itself. Often, the edge of the vocal fold will appear straight because the cyst is embedded in the vocal fold, not arising from the surface.
Speech therapy may get you to your desired voice. If not, surgery is the only option.