I'm in an internship, and I want to quit my job because it is entirely different from the job description. However, my company threatens to give a bad review to the university, ask for a penalty and will harm my career prospects. What should I do?
You don't want to work in a place that is not appropiate for your career regardless of the threats of bad reviews.
I also have a gut feeling that these are void promises. Companies risk losing their collaboration agreement (hence cheap workforce) with the university if their interns have bad experiences there. It seems the company made a mess getting you there and they don't want you to quit so they don't lose the bargain, hence they think you will stay by threatening you.
Report this situation to your university exactly as you are doing here. All the wrongdoing is by that company. State the facts, job is different from the description, company threatened you in giving a bad review if you quit.
They might still give a negative review, but if you have also sent a complaint about the company to the university, they will at most disregard both complaints (no one wants to be part in a labor conflict) or start an audit process to clarify what happened.
The greatest party in loss here is the company, not you. And you have no other choice, staying is going to be harmful for your career and your wellbeing.
Talk to your university.
Assuming you got this internship through your university as part of your studies then your university will be extremely interested to know that the company gave an incorrect job description. Usually that will draw a visit from the university placement coordinator and the possibility that the company will be excluded from future internships. Of course they will want to know details of what you were promised and what you are doing before they take such a step.
You can and should also check with your university what the impact on your studies will be if you change internship. Always do this before changing internships for any reason.
Also your university will tell you the effect of your company giving you a "bad review" (I don't expect it to be much effect under the circumstances).
I think it is entirely normal that a manager will warn you that they will give negative feedback on your internship to your university/school if you decide to up and quit in the middle of your internship.
In my experience, a university or school requests (and requires) feedback and evaluation of you from the company where you intern, which sometimes even results in a passing/failing grade of your internship. You leaving before the end of your internship is something that will and should result in a negative evaluation, because you basically will have failed your internship.
In other words, I think your manager didn't threaten you, they established the consequences of you ending your internship early, so you can make an informed decision.
Your concerns about the internship not matching the description may be valid, but just quitting is not the right reaction for an intern, as it might result in a failing grade. I recommend that you discuss this with a mentor or whoever supervises your internship at the university or school before you end your internship, to see what the effects are of doing this, and whether or not it is a good idea to do so, what alternatives you have, or if it is better to just hold on until the end of the internship. And possibly the university/school can address the mismatch between the description and actual work in a better way than you can.
Here's what I'd do:
I'd focus on getting the replacement job you referenced in your comment, hand in your notice to your current Internship provider and walk away.
You may need to talk with your University if part of your course requirements are tied to your current job - but from your description of what was said to you - it sounds like Piss, Vineagar and Wind (AKA Bluster and BS - they don't want you to go, so are threatening) - hence why I'd just focus on the next opportunity and then resign.
A person is guilty of blackmail if, with a view to gain for himself or another or with intent to cause loss to another, he makes any unwarranted demand with menaces; and for this purpose a demand with menaces is unwarranted unless the person making it does so in the belief—
(a) that he has reasonable grounds for making the demand; and
(b) that the use of the menaces is a proper means of reinforcing the demand.
In this case, the demand is that you involuntarily keep working for the company, and the menaces are that they will try to sabotage your reputation and career if you do not agree.
One factor in whether or not there are reasonable grounds / proper means is whether or not you have a contractual obligation to continue working (e.g. you are attempting to leave in 1 week when the contract requires a 1 month notice period). You didn't specify that level of detail so I'm assuming you do have the contractual right to leave on your proposed last day.