Uh, no. The thing with Nasus is that he needs to use his main farming tool to trade or he will lose trades, and if he uses it to go even in trades it will end with him not scaling as hard into late game.
Nasus is only good in lane against MELEE, AUTOATTACK based champions. Jax is not a good early laner and relies heavily on autos. His counter strike also doesn't block Nasus' Q. Jax is actually probably literally the worst champion to play against Nasus, and you're better off just free farming and hoping you're more skilled late game as they scale pretty equivalently.
As to ways to beat him? You've got:
Ranged harass, like Vlad. Literally anyone with range who doesn't rely on atkspd and speed boosts to kite (Teemo not so much but pretty much any ranged toplane besides), AP is better than AD because it prevents him from getting mileage starting with Iceborn Gauntlet which most nasuses want to build early.
Melee ability based champs. Anyone who doesn't care about his wither. Garen is awesome. Darius. Renekton if you bully really hard and win early. Shyvana is a great pick, as is Mundo. Singed gives him a super hard time. Wukong works great as he can eat nasuses abilities with his decoy
Champs to not pick: Yi, Yasuo, Jax, Irelia, Fiora, Teemo.