Claiming you were fired when in fact you resigned may be defamation: the making of a false factual assertion which damages your reputation (since being fired is generally considered a negative). You could warn the employer that if they tell people this, you will sue them for defamation--then carry out that threat if they continue.
Before doing that: bear in mind that most firings (at least if it's not "for cause"--that is, for something very negative, like insubordination, violating clear company policies, crime at work, etc.) allow the employee to collect unemployment benefits, but that if you resign, you are not eligible for them. Before insisting that you quit or resigned rather than being fired, you may want to consider whether that will cost you any unemployment you might otherwise collect.
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