You're already keeping your boss in the loop (which is essential). But, from comments you've made (like this one below) indicate that you're going to have to be more direct.
Normally I talk to my boss once a week at least. But for example yesterday I had a meeting with him, got him up to date and today (after I had a meeting with my team for the same reason) he approached them and talked with them about the same stuff. But everything was already cleared and new tasks were assigned. So my boss basically just confused everyone because my team thought there are new issues or new tasks. And then I had to resolve and clarify everything again. My team is also wondering why my boss talked to them and not to me, feels like undermining my authority
I think you can use this example when you go to your boss.
Hey boss, yesterday I got you up to date and also met with my team. Then you came in and talked to them and that really muddied up the waters - they thought there was something new that I hadn't assigned. This is a problem.
This makes me feel like you don't trust me to adequately communicate and assign tasks with my team. Is there something going on with my work that you have questions about? Can we talk about that, and find a way to resolve it that also allows me to clearly lead my team?
Then, be quiet and listen. It's possible that your boss does have a problem with something you're doing, and is awkwardly interfering instead of just talking to you about it. It's possible that your boss will realize that his meddling is causing problems and will apologize and let you do your job. Unfortunately, it's also possible that he'll say there is no problem, but he is simply a bad manager who micromanages and causes drama.
If it's the first option, then you can work with him and improve yourself.
If it's the second option, he may need some periodic reminders to get him to change. After the fact, go to him and say something like "Hey, this is an example of something we talked about. It caused confusion again." If he's a good boss, he'll apologize again, and hopefully get better.
If it's the third option (and it kind of sounds like it is), I doubt that talking to him will make much difference. It still might be worth trying.