The phrase "hadst influence" is an old-fashioned way of saying "had influence." If you're looking for synonyms for this phrase, there are plenty of options to choose from. "Exerted influence" is a slightly more formal way of saying the same thing. "Wielded influence" has a bit of a stronger connotation, suggesting that someone had a lot of power and was able to use it effectively. "Had sway over" is another option that implies a great deal of control or persuasion. Finally, "held sway" is a slightly more poetic version of the same phrase. Regardless of which synonym you choose, all of these options convey the idea that someone was able to influence others in some way.