The phrase "hath effect on" is an old, archaic way of saying "has an effect on." There are many synonyms for this phrase that are more commonly used today. Here are a few examples: impacts, affects, influences, alters, changes, modifies, shapes, determines, shapes, directs, regulates, manipulates, sways, persuades, and controls. All of these words convey the idea that something has an effect on something else, whether it be a person, situation, or outcome. It's important to choose the right word for the context and tone of your writing, so understanding these synonyms can be very useful.