The strength/assistance exercise with the biggest carryover to the jerk is probably the push press. Well, besides squats of course! Let’s make that clear, the jerk is a lower body movement. Yes, the bar is in your hands and the weight is supported on locked out arms but the weight gets up there with the power of your legs. If you want your jerk numbers to go up, get your leg strength up. Squat goes up, everything goes up.
Back to the push press. Heavy push presses will teach you how to finish the drive. If you don’t finish that drive and put your leg strength into the bar, the bar isn’t going anywhere. It will also reinforce proper bar path and improve lockout strength.
Strictly for carryover to the jerk, your grip width on your push press, push jerk, and split jerk should all be the same. You’ve probably seen that complex. The push press, push jerk, split jerk 1RM or similar. I’ve had multiple lifters PR their push press doing it. By moving their push press grip out to match their jerk grip there’s less distance to lock the bar out. Admittedly that complex gets you to really drive the crap out of the bar.
Most of the time in weightlifting, you want your assistance work to mimic the full movement as much as possible. Unless you are bringing up a specific weakness. You want your deadlifts and pulls to hit the same positions and your snatch and clean. You also want your overhead work to have the same grip and bar path as your jerk. Strengthening good positions and ingraining motor patterns.
In closing, fix your hand placement, drill good positions, and always do your squats!