Characters who are assertive and take control. Alpha males are dominant, confident, and motivated – all qualities that can be admired or disliked by different people. In fiction with animal characters, alpha animals often lead the whole pack or herd in some way as a leader archetype. The story is not usually about them tearing people apart for the sake of it but rather they’re leading because of an ability to think intelligently on their feet and create plans for a better life. They are always striving to improve themselves too which means they’re often at odds with those who may not want to change such as lower ranking clan members or society’s outsiders like misfits or banished witches/devils/creatures from other realms who have been ostracized.
Alpha characters are about a balance between being powerful and keeping a level head. You can have them be the biggest, meanest brawler in town but if they let their emotions get out of hand from time to time then they’re not going to command as much authority as someone who has learned how to use power responsibly. In other words, you have to learn how to walk the fine line between being pushy and domineering without having your character come off as a jerk who gets his way because he breaks things. Even if alpha characters are intimidating, they’re not all that popular or well-liked by their own kind.