I'm working on a project which uses OpenSSL 1.1.1g. For security and compliance reasons, it is built with SSL and TLS < 1.2 methods compiled out, using the following OpenSSL build options:

no-ssl no-ssl3 no-tls1 no-tls1_1 no-ssl3-method no-tls1-method no-tls1_1-method

When compiling Python v3.8.2 with CFLAGS="-DOPENSSL_NO_SSL2 -DOPENSSL_NO_SSL3 -DOPENSSL_NO_TLS1 -DOPENSSL_NO_TLS1_1" and --with-openssl=/path/to/custom/openssl, _ssl.c fails to compile with the following error:

gcc -pthread -fPIC -Wno-unused-result -Wsign-compare -DNDEBUG -g -fwrapv -O3 -Wall -DOPENSSL_NO_SSL2 -DOPENSSL_NO_SSL3 -DOPENSSL_NO_TLS1 -DOPENSSL_NO_TLS1_1 -DOPENSSL_NO_SSL2 -DOPENSSL_NO_SSL3 -DOPENSSL_NO_TLS1 -DOPENSSL_NO_TLS1_1 -std=c99 -Wextra -Wno-unused-result -Wno-unused-parameter -Wno-missing-field-initializers -Werror=implicit-function-declaration -I./Include/internal -I/home/mitch/openssl/include -I./Include -I. -I/usr/include/x86_64-linux-gnu -I/usr/local/include -I/home/mitch/cpython/Include -I/home/mitch/cpython -c /home/mitch/cpython/Modules/_ssl.c -o build/temp.linux-x86_64-3.8/home/mitch/cpython/Modules/_ssl.o
/home/mitch/cpython/Modules/_ssl.c: In function ‘_ssl__SSLContext_impl’:
/home/mitch/cpython/Modules/_ssl.c:3088:27: error: implicit declaration of function ‘TLSv1_method’; did you mean ‘DTLSv1_method’? [-Werror=implicit-function-declaration]
         ctx = SSL_CTX_new(TLSv1_method());
                           ^~~~~~~~~~~~
                           DTLSv1_method
/home/mitch/cpython/Modules/_ssl.c:3088:27: warning: passing argument 1 of ‘SSL_CTX_new’ makes pointer from integer without a cast [-Wint-conversion]
In file included from /home/mitch/cpython/Modules/_ssl.c:62:0:
/home/mitch/openssl/include/openssl/ssl.h:1503:17: note: expected ‘const SSL_METHOD * {aka const struct ssl_method_st *}’ but argument is of type ‘int’
 __owur SSL_CTX *SSL_CTX_new(const SSL_METHOD *meth);
                 ^~~~~~~~~~~
/home/mitch/cpython/Modules/_ssl.c:3091:27: error: implicit declaration of function ‘TLSv1_1_method’; did you mean ‘TLSv1_2_method’? [-Werror=implicit-function-declaration]
         ctx = SSL_CTX_new(TLSv1_1_method());
                           ^~~~~~~~~~~~~~
                           TLSv1_2_method
/home/mitch/cpython/Modules/_ssl.c:3091:27: warning: passing argument 1 of ‘SSL_CTX_new’ makes pointer from integer without a cast [-Wint-conversion]
In file included from /home/mitch/cpython/Modules/_ssl.c:62:0:
/home/mitch/openssl/include/openssl/ssl.h:1503:17: note: expected ‘const SSL_METHOD * {aka const struct ssl_method_st *}’ but argument is of type ‘int’
 __owur SSL_CTX *SSL_CTX_new(const SSL_METHOD *meth);
                 ^~~~~~~~~~~
cc1: some warnings being treated as errors

This also affects older versions. With v3.5.6, the _ssl module compiles successfully (it may be getting the declaration of TLSv1_method from the system default OpenSSL header since the --with-openssl option doesn't exist in this version), but importing the module at runtime fails:

root@10:/tmp/acmstest# python3
Python 3.5.6 (default, Mar 23 2020, 05:11:33)
[GCC 8.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import ssl
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3.5/ssl.py", line 99, in <module>
    import _ssl             # if we can't import it, let the error propagate
ImportError: /usr/lib/python3.5/lib-dynload/_ssl.cpython-35m-aarch64-linux-gnu.so: undefined symbol: TLSv1_method