How to deal with unruly, unengaged students who complain about me? I got a job 6 months ago as a university lecturer. I was assigned two subjects with the same students. Due to COVID-19, classes are online and lectures are recorded.
From the beginning, the majority of the class was ill-mannered. They would make noise by opening microphones, opening cameras, removing other students, muting my mic.  When I threatened to involve the chairman, they said &quot;he is our buddy.&quot;
So I made some rules, threatening to mark students absent if this continued. The whole class then requested a meeting and asked me to discard these rules. I agreed. Since then, the students have largely stopped their shenanigans with the microphone and camera. But only a few are engaging with the material and answering or asking questions during lecture.
I try calling on them one by one, to ask if there is any confusion, and they always say they don't understand anything. This hurt my feelings. So I said them that tell me that will they be responsive in my class or I will talk to chairman. No one replied except one student, who said &quot;as you wish.&quot;
I called chairman I was about to start my point but before that he told me: be soft with your class, they have issues with you, they have complained to me and sent me a recording. He said that he didn't watch the recording, but I should be careful.
I asked one student (the one who instigated the discussion about the rules) whether they still have an issue with me, and she said no. I said asked why she complained about me when issues were resolved among us. She denied making the complaint. But clearly someone has a grudge against me.
I am really hurt by these allegations. The situation is getting worse day by day.
Did I do something wrong? What should I do differently? Should I be worried about losing my job?
From the beginning, the majority of the class was ill-mannered. They would make noise by opening microphones, opening cameras, removing other students, muting my mic.

This seems like a technical problem; I really can't believe any modern software wouldn't have a way to disallow this behavior. I would start by investigating this.

When I threatened to involve the chairman, they said &quot;he is our
buddy.&quot;

This seems like a bit of an illogical response on your part. Classroom control is your responsibility. What do you expect the chairman to do?

So I made some rules, threatening to mark students absent if this continued. The whole class then requested a meeting and asked me to discard these rules. I agreed.  Since then, the students have largely stopped their shenanigans with
the microphone and camera. But only a few are engaging with the
material and answering or asking questions during lecture.

In general, setting draconian rules and then repealing them entirely will make you seem erratic. In this case, it is true that students muting your microphone and expelling each other during lecture is a serious problem that you have to solve &quot;at any cost.&quot; Still, it seems like there had to have been a better option. Do your colleagues have this problem? How have they dealt with it?

I try calling on them one by one, to ask if there is any confusion, and they always say they don't understand anything.

So, this is the crux of the matter: I suspect your lectures are completely incomprehensible. Reasons I suspect this:

Your students are outright telling you &quot;I don't understand anything.&quot;
It would explain your students' antics with the microphone.
You had extreme difficulty in formulating your question here -- both language-agnostic skills (filtering the important information, organizing it, even breaking into paragraphs) and English-specific syntax.

Now I could be wrong, so I suggest you start by getting a colleague to sit in on your lecture and give you some honest feedback. If I am right, I can't tell you how to improve your teaching, but I think you need to take drastic action -- anything from getting better teaching mentorship to signing up for education classes could be worth trying.

This hurt my feelings. So I said them that tell me that will they be responsive in my class or I will talk to chairman. No one replied except one student, who said &quot;as you wish.&quot;
I called chairman I was about to start my point but before that he told me: be soft with your class, they have issues with you, they have complained to me and sent me a recording. He said that he didn't watch the recording, but I should be careful.

Yeah, two issues here:

You can't force student engagement. Chastising them will only make matters worse. You could try making participation part of their grade; however, I would first make sure your lectures are good, otherwise students will be rightfully angry that you are forcing them to participate in incomprehensible lectures. You may be better off just working with the students who do engage and allowing the others to sit in silence (which is what the chairman suggested).
Threatening to go to the chairman clearly has no effect -- the students don't seem to care and the chairman does not seem to be on your side.


I asked one student (the one who instigated the discussion about the rules) whether they still have an issue with me, and she said no. I said asked why she complained about me when issues were resolved among us. She denied making the complaint. But clearly someone has a grudge against me.

Major mistake -- this will give the impression that you are angry with the students for going to the chairman. Further, due to the power imbalance, it is inappropriate to single out a student in the way that you did. While it would be nice if students resolved their complaints with you rather than going to the chairman, students do have the right to complain about you, and the optics of chastising students for doing so are horrible.

I am really hurt by these allegations. The situation is getting worse day by day.
Did I do something wrong? What should I do differently? Should I be worried about losing my job?

A good rule of thumb is that it's normal for a few students to be unhappy with you (maybe even more than a few, under certain circumstances), but a serious problem if the majority of the students are unhappy with you. Since the class seems to be pretty unanimously against you, I think you need to make some changes.
My recommendations:

Solve your technical problems with the online system.
Get a colleague to give you some honest feedback about the quality of your lectures. If they are bad, take drastic action to improve them (note, this could take years).
Stop trying to control the students' behavior. Focus your energies on giving good lectures and assessing their learning fairly.