I have been offered a job, and the joining company CEO wants references, but I've only worked at two companies and exited each after a big fight with management. If I can't provide references, I won't get an offer letter.
What are my options?
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I've actually read the original post (before dan1111 edit) and I think perhaps you should start by making some self-assessment on the way you deal with people.
Sometimes speaking louder, more often, or more aggressively can get you far (unfortunately), particularly if you come from a privileged background. However that does not make you better at your job, just more visible. For example, you've spoken very highly of your skills but looking at your SO account there is nothing noteworthy. At least in the positive. In one of your own questions you actually seem to disrespect or ignore people that were trying to help you (with no gain for themselves).
Were I the one evaluating you for a new position I would think about the following points (among others):
1) Is this person going to create a toxic environment?
2) Does this person have the required technical skills for the job?
3) Is this person able to be pragmatic when deadlines are approaching?
I'm not sure you would be able to pass 2 out of 3 (although admittedly analyzing an SO profile is very insufficient).
If you really want to turn the page you need to stop being confrontational. Your deeds, not your mouth, will demonstrate your skill. When you propose ideas, you do just that and do not try to enforce their realization by means of verbal or physical intimidation. If the arguments are good most people will see reason.
If I were you my first step would be to go back to the beginning. Get in touch with your previous colleagues. Explain your circumstances, apologize for whatever you need to apologize, and ask for their support namely by means of a reference. And above all try to be honest in the mentioned conversations.
References don't have to be managers, they probably should not be. Managers are usually contacted separately in the background check whether you use them as a reference or not. Often they are constrained from saying anything other than your dates of employment and may possibly answer if they would rehire you. If you have no coworkers who can vouch for the quality of your work, then you have a real problem as you are not as well qualified as you seem to think. If necessary, at this stage of your career, you could get some academic references.
YOU can explain the difficulties you had in your previous jobs and what you have learned to do differently and someone might take a chance on you if they believe you have learned to do better.
Have read the question before it was edited, you need to grow up and learn that your first priority at work is to make your boss happy. EVERYTHING else is secondary to that. Since you have had two unsuccessful attempts at a job (And you are blaming everyone except yourself), you are in the bottom 5% of people most good companies would want to hire. You are going to need to find a less picky place and then you are going to need to do everything in your power to work cooperatively with your colleagues and particularly your boss.
As a junior with a poor track record, you need to stop making suggestions for improvement. Period. None at all. This is because you have no track record to give people reason to believe you are right and you have to learn to get along with people as your first priority. Then you need to learn more effective methods for presenting suggestions for change and you need to earn that no one has 100% of those suggestions accepted so you need to learn to take a rejection of a possible change gracefully. Workplaces are not test beds where you get to do whatever you want, you need to learn to take direction before you try to give direction. There is no perfect workplaces, no places that do nothing that you will disagree with. This is true for everyone.
So you did not get along with your boss at your first job. And then you did not get along with your boss at your second job. And then you lied on your resume.
I don't know how we could help you. We cannot make a good reference appear if you have none. Either you try to find some (maybe former disgruntled co-workers will give you a good one?) or try to find companies that don't require references.