Backport PR pandas-dev#54625: BUG: Fix error in printing timezone series

doc/source/whatsnew/v2.1.0.rst

@@ -667,6 +667,7 @@ Datetimelike
 - Bug in constructing a :class:`Timestamp` from a string representing a time without a date inferring an incorrect unit (:issue:`54097`)
 - Bug in constructing a :class:`Timestamp` with ``ts_input=pd.NA`` raising ``TypeError`` (:issue:`45481`)
 - Bug in parsing datetime strings with weekday but no day e.g. "2023 Sept Thu" incorrectly raising ``AttributeError`` instead of ``ValueError`` (:issue:`52659`)
+- Bug in the repr for :class:`Series` when dtype is a timezone aware datetime with non-nanosecond resolution raising ``OutOfBoundsDatetime`` (:issue:`54623`)
 
 Timedelta
 ^^^^^^^^^

pandas/io/formats/format.py

@@ -1830,8 +1830,8 @@ def get_format_datetime64_from_values(
 class Datetime64TZFormatter(Datetime64Formatter):
     def _format_strings(self) -> list[str]:
         """we by definition have a TZ"""
+        ido = is_dates_only(self.values)
         values = self.values.astype(object)
-        ido = is_dates_only(values)
         formatter = self.formatter or get_format_datetime64(
             ido, date_format=self.date_format
         )

pandas/tests/io/formats/test_format.py

@@ -3320,6 +3320,14 @@ def format_func(x):
         result = formatter.get_result()
         assert result == ["10:10", "12:12"]
 
+    def test_datetime64formatter_tz_ms(self):
+        x = Series(
+            np.array(["2999-01-01", "2999-01-02", "NaT"], dtype="datetime64[ms]")
+        ).dt.tz_localize("US/Pacific")
+        result = fmt.Datetime64TZFormatter(x).get_result()
+        assert result[0].strip() == "2999-01-01 00:00:00-08:00"
+        assert result[1].strip() == "2999-01-02 00:00:00-08:00"
+
 
 class TestNaTFormatting:
     def test_repr(self):