Hello! I'm using specifically crafted Python 3.7.1 for NT 5.2 x86 (Server 2003 R2) and cannot upgrade Python to later versions.
I always building OpenSSL myself using compatible version of MSYS2 with perl 5.22.
Compiled DLLs of OpenSSL 1.1.1k works fine for me (libcrypto-1_1.dll and libssl-1_1.dll in C:\Python37\DLLs\).
But when I try building OpenSSL 3.0.0 alpha 16 (repacing libcrypto-3.dll with libcrypto-1_1.dll and libssl-3.dll with libssl-1_1.dll in
Makefile and util\mkdef.pl) I got this error because of OpenSSL 3.0 backwards incompatibility:

import ssl
File "C:\Python37\lib\ssl.py", line 98, in <module>
import _ssl (C:\Python37\DLLs\_ssl.pyd) # if we can't import it, let the error propagate
ImportError: DLL load failed: The specified procedure could not be found.

What could I do to fix it? Thanks in advance!

Python 3.7 is in security fix-only mode and will not get support for OpenSSL 3.0.0. Only Python 3.8, 3.9, 3.10 beta, and main branch contain OpenSSL 3.0.0 compatibility patches.

Got it but this is a sad news for me...

OpenSSL 3.0.0 is in alpha phase, which means it is unstable, experimental, and not designed for end-users or production use. I recommend that you stick to OpenSSL 1.1.1. It will be supported until September 2023.