As for the third company, you didn't sign a contract at all and didn't apply for social security, so it won't be recorded in your personal file. In this case, you can make appropriate changes to your resume.
But if the law stipulates that the employee's contract is forged, the enterprise has the right to dismiss the employee. As long as the enterprise does some pre-job investigation on the entrants, there will be no problem. Pre-job investigation is usually a high-end position, which is specially done by headhunting companies or recruitment departments. Ordinary employees usually do not do this investigation.