If Beth is a knight, then she told the truth that Cory is also a knight. She says the colour is either yellow, green or red, Cory says it is yellow, white or red, so for both of these to be true the correct potion must be yellow or red. Cory also told the truth when he said Dan is a liar. Ethan agrees that Dan is a liar, so Ethan is not a liar. We already have two Knights (Cory and Beth), so Ethan must be a Knave. Ethan tells the truth with his second sentence ("I'm not a Liar but Dan is"), so to alternate he has to lie when he says the colour is "not green". Therefore the colour must be green, Cory has lied, and therefore so has Beth.

If Beth is a liar, she lied when she called Cory a knight, so Cory is not a knight. Beth also lied with the potion colours, so you do not want to drink yellow, green or red. Cory also says that the colour is not green, so he tells the truth here and can not be a liar. Cory is therefore a knave. But his previous statement "you [Dan] are a liar, I'm not though" is also true. So he can not be a knave because he does not strictly alternate between truth and lies. Therefore Beth is not a Liar, as Cory would cease to exist.

If Beth is a knave and told the truth in her second statement, then Cory is indeed a knight. Cory told the truth that the colour is "yellow, white or red, not green". Beth must have lied in her first statement when she said the colour is "yellow, green or white". If the colour is not yellow, green or white, the colour must be red. Cory told the truth when he said Dan is a liar. Ethan agrees that Dan is a liar, so Ethan is not a liar. Ethan therefore told the truth in his second statement. In his first statement he said it is red or purple, which is true. So Ethan must be a knight, because he does not alternate. But Ethan's third statement says the colour is not yellow, green or red, which is a lie, meaning he is not a knight. Pop, now Ethan doesn't exist.

If Beth is a knave and told the truth in her first statement, the colour is either yellow, green or red. She then lied in her second statement when she said Cory is a knight. So Cory is not a knight. Fred lied when he said it is black or white, so is not a knight. Abe said Cory or Fred is a knight, so he lied and is not a knight. Dan and Ethan must therefore be knights, as the others have been proven not to be. Since Dan is a knight, he called Ethan a liar, and this must be true. But Ethan is also a knight.