Where is the SQL 2012 EXPRESS Edition Service Pack?

You should install SP4 first (https://www.microsoft.com/en-us/download/details.aspx?id=56042)
And then you may apply the KB4583465 (https://www.microsoft.com/en-us/download/details.aspx?id=102625)

That didn't work either. Same result....

I would try running SP3 CU10 update first.
KB4025925 - Cumulative update 10 for SQL Server 2012 SP3 (microsoft.com) 

Then try installing the SP4.

I had already tried that, as well.

If the error says the expected version is 11.0.7001.0  then it means you were attempting to install the KB4583465 first.
What file from the download page did you try to install?

If you are sure the installed package is the right one then it is possible bug at Microsoft side.

When did you restart the last time? Did you try all SP3 CUs? 

Check it from here: https://www.microsoft.com/en-us/download/details.aspx?id=56042

@Priyanka: This link was proposed in the first answer already... (I see you are the writer but you could also read what others wrote :-)

Anything else?

You could answer my earlier question:
What file from the download page did you try to install?

Okay, okay.  I started my day yesterday by downloading and installing SQL 2012 Express Edition which including service pack 3.
Then, I installed SQL 2012 service pack 4 GDR.  When I conducted a search and found the page pointing me to that, Google told me that it works for SQL Express.  That's not true, as I later found.
So, I took the advice earlier in this post and installed service pack 4.
From there, I installed whatever else was suggested at the beginning of this post.

OK, it seems the SP4 GDR was installed correctly at the end and everything is working now.

The SP4 GDR is just a hotfix and the download page states "this update requires SP4 to be installed first"... and it was also proposed as the first answer :-)

No, I didn't say that this is fixed.  The issue remains.
Where in the world did you get the idea that I said that the issue no longer exists???????????????

I've asked simple question  "What file from the download page did you try to install?"
And you did not answer that so it could mean you don't need to answer this simple question because everything works.
The list of files available for download is here:

BTW your post states: "So, I took the advice earlier in this post and installed service pack 4."  no error is mentioned here...  So do you have SP4 installed or not?

I tried to install SP4 and got the issue that I mentioned yesterday.  
No, I have not tried uninstalling and reinstalling SQL 2012 Express with service pack 4.  I'll try this, as soon as possible.
Thank you!

I am not sure you've been installing SQL Express with SP4 because
1. You did not disclose what file was downloaded from the Microsoft site
2. You did not show any error message from SP4 installation (the image showed in your post was from the attempt to install  SP4-GDR (KB4583465) over the SP3 which must not work..

I've tested the SP4 installation and the final version is:
Microsoft SQL Server 2012 (SP4) (KB4018073) - 11.0.7001.0 (X64)   Aug 15 2017 10:23:29   Copyright (c) Microsoft Corporation  Express Edition (64-bit) on Windows NT 6.3 <X64> (Build 19043: )

The successive SP4-GDR installation to above version upgraded the version to:
Microsoft SQL Server 2012 (SP4-GDR) (KB4583465) - 11.0.7507.2 (X64)   Nov  1 2020 00:48:37   Copyright (c) Microsoft Corporation  Express Edition (64-bit) on Windows NT 6.3 <X64> (Build 19043: )

Everything worked smoothly w/o any error or break.

I was successful, just now, in uninstalling and reinstalling SQL 2012 Express with service pack 4 and then the required update.
Thank you, for your help!

Great!