Jax is a hypercarry, his early game is a lot weaker, the items he builds tend to be on the expensive side so denying him CS should be a priority, pick a lane bully and you should be able to force him out of lane or kill him early on to deny levels and gold. If you want specific picks to counter him then Jayce deals with him pretty well, he can harass him in cannon form whenever he tries to CS, and can swap to hammer form to knock him away and deny the stun as well as the follow up damage, just don't swap forms for no reason since it creates a window where a good Jax can punish you. Fiora is somewhat even with Jax, she is auto attack based so his E can deny some damage, but she can also W to stun him and turn trades in her favor, she will outsustain Jax in both health and mana, and her early trades hit him pretty hard. Renekton is probably the best lane bully to pick vs him, he can dash to avoid stuns or stick to you, sustains incredibly well, and deals great early damage. Aside from that you could pick any of the juggernauts, they have strong enough early games to shut jax down hard.