diff --git a/.flake8 b/.flake8
index 4e487c57..76ddaa85 100644
--- a/.flake8
+++ b/.flake8
@@ -10,8 +10,9 @@ select = A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,B901,B902,B903,B950
 # W503: Mutually exclusive with W504.
 ignore = E226,E501,E722,W503
 per-file-ignores =
+    # B011: assert False used for coverage skipping
     # S101: Pytest uses assert
-    tests/*:S101
+    tests/*:B011,S101
 
 # flake8-import-order
 application-import-names = aiohttp_security
diff --git a/aiohttp_security/jwt_identity.py b/aiohttp_security/jwt_identity.py
index 6edcf69e..b322cda9 100644
--- a/aiohttp_security/jwt_identity.py
+++ b/aiohttp_security/jwt_identity.py
@@ -2,7 +2,7 @@
 
 """
 
-from typing import Optional
+from typing import Optional, Tuple, Type
 
 from aiohttp import web
 
@@ -11,14 +11,23 @@
 try:
     import jwt
     HAS_JWT = True
+    _bases_error: Tuple[Type[jwt.exceptions.PyJWTError], ...]
+    _bases_error = (jwt.exceptions.PyJWTError,)
 except ImportError:  # pragma: no cover
     HAS_JWT = False
+    _bases_error = ()
 
 
 AUTH_HEADER_NAME = 'Authorization'
 AUTH_SCHEME = 'Bearer '
 
 
+# This class inherits from ValueError to maintain backward compatibility
+# with previous versions of aiohttp-security
+class InvalidAuthorizationScheme(ValueError, *_bases_error):  # type: ignore[misc]
+    """Exception when the auth method can't be read from header."""
+
+
 class JWTIdentityPolicy(AbstractIdentityPolicy):
     def __init__(self, secret: str, algorithm: str = "HS256", key: str = "login"):
         if not HAS_JWT:
@@ -34,8 +43,8 @@ async def identify(self, request: web.Request) -> Optional[str]:
             return None
 
         if not header_identity.startswith(AUTH_SCHEME):
-            raise ValueError("Invalid authorization scheme. "
-                             + "Should be `{}<token>`".format(AUTH_SCHEME))
+            raise InvalidAuthorizationScheme("Invalid authorization scheme. "
+                                             "Should be `{}<token>`".format(AUTH_SCHEME))
 
         token = header_identity.split(' ')[1].strip()
 
diff --git a/tests/test_jwt_identity.py b/tests/test_jwt_identity.py
index b4ed430c..0b9cd207 100644
--- a/tests/test_jwt_identity.py
+++ b/tests/test_jwt_identity.py
@@ -80,3 +80,28 @@ async def check(request):
     resp = await client.get('/', headers=headers)
     assert 400 == resp.status
     assert 'Invalid authorization scheme' in resp.reason
+
+
+async def test_identify_expired_signature(make_token, aiohttp_client):
+    kwt_secret_key = "Key"  # noqa: S105
+
+    token = make_token({"login": "Andrew", "exp": 0}, kwt_secret_key)
+
+    async def check(request):
+        policy = request.app[IDENTITY_KEY]
+        try:
+            await policy.identify(request)
+        except jwt.exceptions.PyJWTError as exc:
+            raise web.HTTPBadRequest(reason=str(exc))
+
+        assert False
+
+    app = web.Application()
+    _setup(app, JWTIdentityPolicy(kwt_secret_key), Autz())
+    app.router.add_route("GET", "/", check)
+
+    client = await aiohttp_client(app)
+    headers = {"Authorization": "Bearer {}".format(token)}
+    resp = await client.get("/", headers=headers)
+    assert 400 == resp.status
+    assert "Signature has expired" in resp.reason