Against kassadin, Kassadin is at his weakest in the early game. Try to fight as much as possible so he falls behind.

Post level 6, if you have any CC abilities, do not use them unless his Ultimate k is down as he will use their cooldowns to play aggressive and trade with you. 

Kassadin lacks wave clear in the early game. If you can keep the wave closer to your side of the map early on, it will be very difficult for him to farm or break your freeze. If he does walk up to last hit, you can look to trade with him. Against kassadin, Kassadin is at his weakest in the early game. Try to fight as much as possible so he falls behind. Position level 6, if you have CC capabilities, don't use them unless his Ultimate k is down because he will use their cooldowns to play aggressive and trade with you. Kassadin lacks clear vague in the early game. If you can keep the wave closer to your side of the card early, it will be very difficult for him to close or break your freeze. If he walks up to the last hit, you can watch to trade with him.