diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 5bae3bee..98925166 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -1,3 +1,8 @@
+v4.18.2
+=======
+
+* Fix an additional regression with the deprecated ``jsonschema.RefResolver`` and pointer resolution.
+
 v4.18.1
 =======
 
diff --git a/jsonschema/tests/test_validators.py b/jsonschema/tests/test_validators.py
index 5a4f87f3..ca03efd4 100644
--- a/jsonschema/tests/test_validators.py
+++ b/jsonschema/tests/test_validators.py
@@ -2394,6 +2394,25 @@ def handle(uri):
             (False, True),
         )
 
+    def test_refresolver_with_pointer_in_schema_with_no_id(self):
+        """
+        See https://github.com/python-jsonschema/jsonschema/issues/1124#issuecomment-1632574249.
+        """  # noqa: E501
+
+        schema = {
+            "properties": {"x": {"$ref": "#/definitions/x"}},
+            "definitions": {"x": {"type": "integer"}},
+        }
+
+        validator = validators.Draft202012Validator(
+            schema,
+            resolver=validators._RefResolver("", schema),
+        )
+        self.assertEqual(
+            (validator.is_valid({"x": "y"}), validator.is_valid({"x": 37})),
+            (False, True),
+        )
+
 
 
 def sorted_errors(errors):
diff --git a/jsonschema/validators.py b/jsonschema/validators.py
index b8a9c141..60c19821 100644
--- a/jsonschema/validators.py
+++ b/jsonschema/validators.py
@@ -278,7 +278,9 @@ def __attrs_post_init__(self):
             # REMOVEME: Legacy ref resolution state management.
             push_scope = getattr(self._ref_resolver, "push_scope", None)
             if push_scope is not None:
-                push_scope(id_of(self.schema))
+                id = id_of(self.schema)
+                if id is not None:
+                    push_scope(id)
 
         @classmethod
         def check_schema(cls, schema, format_checker=_UNSET):