diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index b696447d0982b7..ba51b9c3e066b5 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -3691,6 +3691,29 @@ def test_errors(self):
             class D(UserName):
                 pass
 
+    def test_or(self):
+        UserId = NewType('UserId', int)
+        UserName = NewType('UserName', str)
+
+        for cls in (int, UserName):
+            with self.subTest(cls=cls):
+                self.assertEqual(UserId | cls, Union[UserId, cls])
+                self.assertEqual(cls | UserId, Union[cls, UserId])
+
+                self.assertEqual(get_args(UserId | cls), (UserId, cls))
+                self.assertEqual(get_args(cls | UserId), (cls, UserId))
+
+    def test_special_attrs(self):
+        UserId = NewType('UserId', int)
+
+        self.assertEqual(UserId.__name__, 'UserId')
+        self.assertEqual(UserId.__qualname__, 'UserId')
+        self.assertEqual(UserId.__module__, __name__)
+
+    def test_repr(self):
+        UserId = NewType('UserId', int)
+
+        self.assertEqual(repr(UserId), f'{__name__}.UserId')
 
 class NamedTupleTests(BaseTestCase):
     class NestedEmployee(NamedTuple):
diff --git a/Lib/typing.py b/Lib/typing.py
index 4a6efee802042b..1aff0a1b3026d5 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -1374,6 +1374,12 @@ def _no_init(self, *args, **kwargs):
     if type(self)._is_protocol:
         raise TypeError('Protocols cannot be instantiated')
 
+def _callee(depth=2, default=None):
+    try:
+        return sys._getframe(depth).f_globals['__name__']
+    except (AttributeError, ValueError):  # For platforms without _getframe()
+        return default
+
 
 def _allow_reckless_class_checks(depth=3):
     """Allow instance and class checks for special stdlib modules.
@@ -2350,7 +2356,7 @@ class body be required.
 TypedDict.__mro_entries__ = lambda bases: (_TypedDict,)
 
 
-def NewType(name, tp):
+class NewType:
     """NewType creates simple unique types with almost zero
     runtime overhead. NewType(name, tp) is considered a subtype of tp
     by static type checkers. At runtime, NewType(name, tp) returns
@@ -2369,12 +2375,23 @@ def name_by_id(user_id: UserId) -> str:
         num = UserId(5) + 1     # type: int
     """
 
-    def new_type(x):
+    def __init__(self, name, tp):
+        self.__name__ = name
+        self.__qualname__ = name
+        self.__module__ = _callee(default='typing')
+        self.__supertype__ = tp
+
+    def __repr__(self):
+        return f'{self.__module__}.{self.__qualname__}'
+
+    def __call__(self, x):
         return x
 
-    new_type.__name__ = name
-    new_type.__supertype__ = tp
-    return new_type
+    def __or__(self, other):
+        return Union[self, other]
+
+    def __ror__(self, other):
+        return Union[other, self]
 
 
 # Python-version-specific alias (Python 2: unicode; Python 3: str)
diff --git a/Misc/NEWS.d/next/Library/2021-07-19-22-43-15.bpo-44353.HF81_Q.rst b/Misc/NEWS.d/next/Library/2021-07-19-22-43-15.bpo-44353.HF81_Q.rst
new file mode 100644
index 00000000000000..8a1e0f77b31772
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-07-19-22-43-15.bpo-44353.HF81_Q.rst
@@ -0,0 +1,2 @@
+Refactor ``typing.NewType`` from function into callable class. Patch
+provided by Yurii Karabas.
diff --git a/Parser/pegen.c b/Parser/pegen.c
index 3e8ddfbf53cf75..106dba9ab49ad3 100644
--- a/Parser/pegen.c
+++ b/Parser/pegen.c
@@ -402,7 +402,7 @@ _PyPegen_byte_offset_to_character_offset(PyObject *line, Py_ssize_t col_offset)
 {
     const char *str = PyUnicode_AsUTF8(line);
     if (!str) {
-        return 0;
+        return -1;
     }
     Py_ssize_t len = strlen(str);
     if (col_offset > len + 1) {
@@ -411,7 +411,7 @@ _PyPegen_byte_offset_to_character_offset(PyObject *line, Py_ssize_t col_offset)
     assert(col_offset >= 0);
     PyObject *text = PyUnicode_DecodeUTF8(str, col_offset, "replace");
     if (!text) {
-        return 0;
+        return -1;
     }
     Py_ssize_t size = PyUnicode_GET_LENGTH(text);
     Py_DECREF(text);
@@ -499,9 +499,17 @@ _PyPegen_raise_error_known_location(Parser *p, PyObject *errtype,
 
     if (p->tok->encoding != NULL) {
         col_number = _PyPegen_byte_offset_to_character_offset(error_line, col_offset);
-        end_col_number = end_col_number > 0 ?
-                         _PyPegen_byte_offset_to_character_offset(error_line, end_col_offset) :
-                         end_col_number;
+        if (col_number < 0) {
+            goto error;
+        }
+        if (end_col_number > 0) {
+            Py_ssize_t end_col_offset = _PyPegen_byte_offset_to_character_offset(error_line, end_col_number);
+            if (end_col_offset < 0) {
+                goto error;
+            } else {
+                end_col_number = end_col_offset;
+            }
+        }
     }
     tmp = Py_BuildValue("(OiiNii)", p->tok->filename, lineno, col_number, error_line, end_lineno, end_col_number);
     if (!tmp) {
diff --git a/Python/traceback.c b/Python/traceback.c
index 643096c81fc8f5..e02caef6f9bce7 100644
--- a/Python/traceback.c
+++ b/Python/traceback.c
@@ -745,7 +745,17 @@ tb_displayline(PyTracebackObject* tb, PyObject *f, PyObject *filename, int linen
     // Convert the utf-8 byte offset to the actual character offset so we print the right number of carets.
     assert(source_line);
     Py_ssize_t start_offset = _PyPegen_byte_offset_to_character_offset(source_line, start_col_byte_offset);
+    if (start_offset < 0) {
+        err = ignore_source_errors() < 0;
+        goto done;
+    }
+
     Py_ssize_t end_offset = _PyPegen_byte_offset_to_character_offset(source_line, end_col_byte_offset);
+    if (end_offset < 0) {
+        err = ignore_source_errors() < 0;
+        goto done;
+    }
+
     Py_ssize_t left_end_offset = -1;
     Py_ssize_t right_start_offset = -1;