Unless they have a password which is currently being used then they are talking nonsense and there's a 99.9% chance they are just relying on online leaked dumps of credentials from service breaches.I also got the same exact email from a guy called zack47 who put down my email address and my password, although i have forgotten if i ever used that password before and have changed it about 3 weeks ago.
Change all of your passwords, make sure your passwords are strong, do not re-use the same passwords and give away as least personal information as you can online. Problem solved. If you really suspect that your system is currently infected, then reset it.
People who have infected someone else with a backdoor will not go around confessing to this and exposing this fact unless they are extremely idiotic. Therefore, someone actually claiming to have infected your system with malicious software is in itself... a sign that they actually didn't and that they are getting the information some other way. Anyway, if they did actually have access to your system and thus all your credentials... they would be able to go on and sell those credentials to other hackers or access your online banking, instead of trying to threaten you on an e-mail, so the chances are slim at best.
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