diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 3fa806ddc2cde7..bd831ac22419af 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -2429,16 +2429,18 @@ def run(self):
                         self.write(msg.lower())
                 except OSError as e:
                     # handles SSLError and socket errors
+                    if isinstance(e, ConnectionError):
+                        # OpenSSL 1.1.1 sometimes raises
+                        # ConnectionResetError when connection is not
+                        # shut down gracefully.
+                        if self.server.chatty and support.verbose:
+                            print(f" Connection reset by peer: {self.addr}")
+
+                        self.close()
+                        self.running = False
+                        return
                     if self.server.chatty and support.verbose:
-                        if isinstance(e, ConnectionError):
-                            # OpenSSL 1.1.1 sometimes raises
-                            # ConnectionResetError when connection is not
-                            # shut down gracefully.
-                            print(
-                                f" Connection reset by peer: {self.addr}"
-                            )
-                        else:
-                            handle_error("Test server failure:\n")
+                        handle_error("Test server failure:\n")
                     try:
                         self.write(b"ERROR\n")
                     except OSError:
@@ -3166,8 +3168,8 @@ def test_wrong_cert_tls13(self):
                                         suppress_ragged_eofs=False) as s:
             s.connect((HOST, server.port))
             with self.assertRaisesRegex(
-                ssl.SSLError,
-                'alert unknown ca|EOF occurred|TLSV1_ALERT_UNKNOWN_CA'
+                OSError,
+                'alert unknown ca|EOF occurred|TLSV1_ALERT_UNKNOWN_CA|closed by the remote host|Connection reset by peer'
             ):
                 # TLS 1.3 perform client cert exchange after handshake
                 s.write(b'data')
@@ -4532,8 +4534,8 @@ def msg_cb(conn, direction, version, content_type, msg_type, data):
                 # test sometimes fails with EOF error. Test passes as long as
                 # server aborts connection with an error.
                 with self.assertRaisesRegex(
-                    ssl.SSLError,
-                    '(certificate required|EOF occurred)'
+                    OSError,
+                    'certificate required|EOF occurred|closed by the remote host|Connection reset by peer'
                 ):
                     # receive CertificateRequest
                     data = s.recv(1024)
diff --git a/Misc/NEWS.d/next/Library/2024-02-18-09-50-31.gh-issue-115627.HGchj0.rst b/Misc/NEWS.d/next/Library/2024-02-18-09-50-31.gh-issue-115627.HGchj0.rst
new file mode 100644
index 00000000000000..75d926ab59d557
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-02-18-09-50-31.gh-issue-115627.HGchj0.rst
@@ -0,0 +1,2 @@
+Fix the :mod:`ssl` module error handling of connection terminate by peer.
+It now throws an OSError with the appropriate error code instead of an EOFError.
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index d00f407b569fb6..f5a79dcb1ac57d 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -599,7 +599,7 @@ PySSL_ChainExceptions(PySSLSocket *sslsock) {
 }
 
 static PyObject *
-PySSL_SetError(PySSLSocket *sslsock, int ret, const char *filename, int lineno)
+PySSL_SetError(PySSLSocket *sslsock, const char *filename, int lineno)
 {
     PyObject *type;
     char *errstr = NULL;
@@ -612,7 +612,6 @@ PySSL_SetError(PySSLSocket *sslsock, int ret, const char *filename, int lineno)
     _sslmodulestate *state = get_state_sock(sslsock);
     type = state->PySSLErrorObject;
 
-    assert(ret <= 0);
     e = ERR_peek_last_error();
 
     if (sslsock->ssl != NULL) {
@@ -645,32 +644,21 @@ PySSL_SetError(PySSLSocket *sslsock, int ret, const char *filename, int lineno)
         case SSL_ERROR_SYSCALL:
         {
             if (e == 0) {
-                PySocketSockObject *s = GET_SOCKET(sslsock);
-                if (ret == 0 || (((PyObject *)s) == Py_None)) {
+                /* underlying BIO reported an I/O error */
+                ERR_clear_error();
+#ifdef MS_WINDOWS
+                if (err.ws) {
+                    return PyErr_SetFromWindowsErr(err.ws);
+                }
+#endif
+                if (err.c) {
+                    errno = err.c;
+                    return PyErr_SetFromErrno(PyExc_OSError);
+                }
+                else {
                     p = PY_SSL_ERROR_EOF;
                     type = state->PySSLEOFErrorObject;
                     errstr = "EOF occurred in violation of protocol";
-                } else if (s && ret == -1) {
-                    /* underlying BIO reported an I/O error */
-                    ERR_clear_error();
-#ifdef MS_WINDOWS
-                    if (err.ws) {
-                        return PyErr_SetFromWindowsErr(err.ws);
-                    }
-#endif
-                    if (err.c) {
-                        errno = err.c;
-                        return PyErr_SetFromErrno(PyExc_OSError);
-                    }
-                    else {
-                        p = PY_SSL_ERROR_EOF;
-                        type = state->PySSLEOFErrorObject;
-                        errstr = "EOF occurred in violation of protocol";
-                    }
-                } else { /* possible? */
-                    p = PY_SSL_ERROR_SYSCALL;
-                    type = state->PySSLSyscallErrorObject;
-                    errstr = "Some I/O error occurred";
                 }
             } else {
                 if (ERR_GET_LIB(e) == ERR_LIB_SSL &&
@@ -1030,7 +1018,7 @@ _ssl__SSLSocket_do_handshake_impl(PySSLSocket *self)
              err.ssl == SSL_ERROR_WANT_WRITE);
     Py_XDECREF(sock);
     if (ret < 1)
-        return PySSL_SetError(self, ret, __FILE__, __LINE__);
+        return PySSL_SetError(self, __FILE__, __LINE__);
     if (PySSL_ChainExceptions(self) < 0)
         return NULL;
     Py_RETURN_NONE;
@@ -2437,7 +2425,7 @@ _ssl__SSLSocket_write_impl(PySSLSocket *self, Py_buffer *b)
 
     Py_XDECREF(sock);
     if (retval == 0)
-        return PySSL_SetError(self, retval, __FILE__, __LINE__);
+        return PySSL_SetError(self, __FILE__, __LINE__);
     if (PySSL_ChainExceptions(self) < 0)
         return NULL;
     return PyLong_FromSize_t(count);
@@ -2467,7 +2455,7 @@ _ssl__SSLSocket_pending_impl(PySSLSocket *self)
     self->err = err;
 
     if (count < 0)
-        return PySSL_SetError(self, count, __FILE__, __LINE__);
+        return PySSL_SetError(self, __FILE__, __LINE__);
     else
         return PyLong_FromLong(count);
 }
@@ -2590,7 +2578,7 @@ _ssl__SSLSocket_read_impl(PySSLSocket *self, Py_ssize_t len,
              err.ssl == SSL_ERROR_WANT_WRITE);
 
     if (retval == 0) {
-        PySSL_SetError(self, retval, __FILE__, __LINE__);
+        PySSL_SetError(self, __FILE__, __LINE__);
         goto error;
     }
     if (self->exc != NULL)
@@ -2716,7 +2704,7 @@ _ssl__SSLSocket_shutdown_impl(PySSLSocket *self)
     }
     if (ret < 0) {
         Py_XDECREF(sock);
-        PySSL_SetError(self, ret, __FILE__, __LINE__);
+        PySSL_SetError(self, __FILE__, __LINE__);
         return NULL;
     }
     if (self->exc != NULL)