Well, you need to create a backstory for this jealous alpha hero. Maybe he had some past experiences that made him insecure in relationships, like being betrayed. In the novel, his jealousy can be expressed through his actions. He might interrupt the heroine's conversations with other men or even try to keep her away from male friends. Also, his dialogue can be very possessive, like 'You're mine and no one else's.'
To write a jealous alpha hero in a romance novel, start with his physical appearance. Make him look strong and imposing. In terms of his jealousy, it should be a complex emotion. It's not just about being possessive. It can also come from his deep love for the heroine. For instance, when he sees the heroine laughing with another man, he might feel a pang of jealousy. He could then take the heroine aside and have an intense conversation about his feelings, explaining that he can't bear to see her with other men because she means so much to him. This way, the readers can understand that his jealousy is a part of his passionate love for the heroine.
First, give him a strong and dominant personality. For example, he might be the CEO of a big company or a powerful figure in society. Then, show his jealousy in situations where the heroine interacts with other men. He could glare at the other guy or be overly possessive of the heroine.