BUG: interpolate raising wrong error for ea (#55347)

doc/source/whatsnew/v2.1.2.rst

@@ -24,6 +24,7 @@ Bug fixes
 ~~~~~~~~~
 - Fixed bug in :meth:`Categorical.equals` if other has arrow backed string dtype (:issue:`55364`)
 - Fixed bug in :meth:`DataFrame.idxmin` and :meth:`DataFrame.idxmax` raising for arrow dtypes (:issue:`55368`)
+- Fixed bug in :meth:`DataFrame.interpolate` raising incorrect error message (:issue:`55347`)
 - Fixed bug in :meth:`DataFrame.resample` not respecting ``closed`` and ``label`` arguments for :class:`~pandas.tseries.offsets.BusinessDay` (:issue:`55282`)
 - Fixed bug in :meth:`DataFrame.resample` where bin edges were not correct for :class:`~pandas.tseries.offsets.BusinessDay` (:issue:`55281`)
 - Silence ``Period[B]`` warnings introduced by :issue:`53446` during normal plotting activity (:issue:`55138`)

pandas/core/arrays/base.py

@@ -893,7 +893,6 @@ def interpolate(
         limit,
         limit_direction,
         limit_area,
-        fill_value,
         copy: bool,
         **kwargs,
     ) -> Self:

pandas/tests/frame/methods/test_interpolate.py

@@ -497,3 +497,9 @@ def test_interpolate_empty_df(self):
         result = df.interpolate(inplace=True)
         assert result is None
         tm.assert_frame_equal(df, expected)
+
+    def test_interpolate_ea_raise(self):
+        # GH#55347
+        df = DataFrame({"a": [1, None, 2]}, dtype="Int64")
+        with pytest.raises(NotImplementedError, match="does not implement"):
+            df.interpolate()