You want to be using Jax's F33 string all the time. It's 9f in startup and has not bad range for what it is. It hits mid and you can hit confirm it into DB4 Amp or BF2 Amp for a launch that you can combo off of. The F3 string in itself is fantastic because the F3 is so fast and mid hitting which allows you to be a force to be reckoned with in the poke battle. The beauty of this string is that you can also use F3 itself as a stagger for pressure, since it recovers pretty quickly. You can use F33 as a stagger too because Jax can condition the opponent to think the overhead ender of the string is coming, which is F331.
F331 is -7 on block so your pressure ends there and your safe if they block it and don't have a 6f poke. There is a gap in F331 just before the overhead hits and your opponent can flawless block punish you for using it. Nevertheless, this adds some more pressure/mindgame potential to the mix because if they're expecting that or attempting to flawless block then you can end the string at F33 and then either go into more F3 pressure or go for a grab.
Jax likes to to throw a lot, mix it in a lot with your F3 pressure.
F3 TL;DR:
-9 frames
-mid
-staggerable
-F33 safe mid hitconfirm
-F331 staggerable each hit
-F331 -7
Midscreen combo:
F33~DB4 Amp, dash, d12, d12~DB1,1,1,1,1, 4
Easy version:
F33~BF2 Amp, dash, d12, d12~DB1,1,1,1,1, 4
Gotcha Grab:
Use 1 for more damage, 2 for corner carry, 3 for a side switch, and 4 to toss them (in the corner it restands)
Corner:
By ending your gotcha grab in the corner, you have a +4 restand so you can frametrap with F3 again. If they jump and you time your F33 right then both hits will connect in a juggle and you can combo into gotcha grab to put them in a restand again. If you mistime your F33 then the first hit will catch them jumping but the second hit will whiff.
Due to being +4, this allows you to frame trap everything in the game pretty much.