Once We Get Married - This c-drama, the ML is very possessive of FL. He gets jealous very easily and once he falls for her, he can't stand being apart from her. So in my opinion he is very possessive of her. It's a cute drama and definitely worth the watch.
Professional Single - This is also a possessive ML drama. Once he falls for her, (which is fairly quickly...) he gets jealous.. a lot. It's quite adorable, nothing toxic here. So, if you're after the ML being jealous, this is the right drama for you.
Assistant of Superstar - This has to be one of my favorite dramas of all time! The ML falls for the FL within the first couple of episodes. Because he fell so fast, he tries to get her to fall for him, and with that of course comes jealousy. But he is also very protective of her in this drama. He doesn't want anything bad to happen to her. He's so possessive of her, he doesn't want her to move out of his house and tries to get her to stay, etc. It's so adorable, I absolutely love it. I 1000/10 recommend.
Moonlight- I always recommend this one if you've seen "Assistant of Superstar." And vice versa. These two dramas give off the same vibe. Both have a famous ML who falls for their "assistant" early on in the drama. He is also very possessive of the FL. He schemes things to get her to come see him. And just like in "Assistant of Superstar", he doesn't want the FL to move out of his house, so he tries to get her to stay.. Overall it's a cute drama, and the ML in this drama, also gets jealous very easily. ;)
Meteor Garden- Out of all that I've mentioned so far, this drama has by far the most possessive and jealous ML. At first he starts out a bit toxic. At the beginning of the drama he's a bit much. He has moments where he gets mad at the FL for hanging with other guys, and also resorts to violence easily. He's known as the "bully" of the school. So when he falls for the FL, he doesn't know how to act. But he gets better as the drama goes on and he becomes such a sweetheart. But if you're looking for a jealous ML, here he is... He gets jealous and possessive sooo easily. Even though it's 50 episodes, it does not feel like that what so ever. It flys by to be honest. Fair warning.... *the couple has a lot of ups and downs in their relationship. The FL does get on your nerves a little bit, so watch out for her. But don't worry they end up together in the end and it's a happy ending.
Please Love Me - At first the ML doesn't like the FL. He is into someone else. But after being rejected multiple times, he comes to realize he likes the FL. Once he realizes it he becomes very jealous of the men around her. One in particular.. the childhood sweetheart... so he tries to win her over despite having the 2ML in the way. This one is definitely worth the watch.
High End Crush - Unlike the others, this is a k-drama. but I added it in because I felt it fit what you were looking for. The ML is sooo possessive of the FL. He goes through great heights to get her to be with his company. He falls for her almost immediately.. lol. He also gets jealous very easily. Overall it's a cute watch.
Skate into Love- I don't know if you would call this one possessive or jealous of sorts, but it gives you the same vibes from a drama that has a possessive and jealous ML. The ML hates the FL at first because she teased him all throughout their younger years, so he plans to get payback. But he eventually falls for her and wants to help her through all her difficulties. There are probably a couple of jealousy scenes, butttt this drama is worth the watch nevertheless.
To Fly With You- This one is a lot like "Skate Into Love" but we have a more jealous ML. I wouldn't label this drama with a possessive/jealous ML, but again; it gives us the same vibes. In the drama, the FLs first crush comes back, and he wants her back. It's here where we see the ML start to get jealous and worry if she is still into her high school crush. This is also worth the watch.