Help In English Please

[Fatemah]

What is the polite way to send a reminder email to a professor, my visa was rejected, then I appealed against this and now the embassy wants a new admission letter issued my university, I wrote an email to the university and told them my whole case, so my course coordinator said the university will not issue a new admission letter but they will issue me a letter which will be that I'm currently enrolled in university and it will help me for my visa, the university said they will issue me the letter on Tuesday but till now I have not got any response from them. Now I want to send them an email and want to ask when they will issue me the letter, is it correct way to ask.
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Dear Madam,
I hope you are having a good week. I would appreciate if you could provide me an update that when I will get the letter, so i have to proper my visa application according to that.

Thanks.

[JimF]

Dear Prof ........,

I hope you are having a good week. I would appreciate it if you could provide me with an update of when I will get the letter, so that I can prepare my visa application accordingly.

Yours sincerely,

[Tuvok]

"the university said they will issue me the letter on Tuesday"

This could be read two ways:

1. you will get the letter on Tuesday
2. they told on you Tuesday that they would give you the letter but you haven't received it yet

If its option 2 then

Dear Madam,
I contacted you on DATE regarding obtaining additional proof of my enrolled status to aid my visa application. I would appreciate if you could provide me an update as to when I will receive the letter in order for me to prepare my visa application accordingly.

Thanks.

[JimF]

"Dear Madam,"

You have got to be joking! Dear Madam?

[Buenchico]

Jim's draft will be perfectly sufficient.

However, for your future reference, Fatemah, I'll mention that in 'business English', it's always considered best to use a person's name (including any academic title, where relevant) where it's known, rather than to use 'Dear Sir' or 'Dear Madam'. So, for example, "Dear Professor Schmidt" or "Dear Dr Müller" is considered much better than "Dear Sir' or "Dear Madam".

Enquiries after a person's health (such as "I hope you are well") or how they're doing (e.g. "I hope that you're having a good week") are considered by some to be inappropriate unless you've already established a personal relationship with the recipient of your correspondence.

My own preference for the content of your email would to be ask (again) for the letter itself (which is what really matters), rather than for an indication of when it might arrive.

So my own wording would be along these lines:
"Dear Professor Schmidt,
I write to remind you that I am awaiting a letter from you, confirming that I am currently enrolled for study at the University of Siegen and fully participating in my studies. I need this letter to reapply for my visa to study in Germany, after my initial application was rejected.

I would be most grateful if you would provide me with this letter at your earliest convenience, as I am becoming concerned that without it I might be forced to abandon my studies.

I offer my thanks in anticipation of your kind assistance in this matter.

Regards

Fatemah X"

[Fatemah]

Thank you so much for your suggestions and help everyone.
Thank you so much for the correction @Buenchico
, i always think that writing Prof/teacher name is disrespectful :-) But I will now careful and will follow your instructions thank you :)