diff --git a/pandas/_typing.py b/pandas/_typing.py
index 2b42a0a3efb44..8cab908d62507 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -307,10 +307,12 @@ def closed(self) -> bool:
 XMLParsers = Literal["lxml", "etree"]
 
 # Interval closed type
-
 IntervalClosedType = Literal["left", "right", "both", "neither"]
 
 # datetime and NaTType
-
 DatetimeNaTType = Union[datetime, "NaTType"]
 DateTimeErrorChoices = Literal["ignore", "raise", "coerce"]
+
+# sort_index
+SortKind = Literal["quicksort", "mergesort", "heapsort", "stable"]
+NaPosition = Literal["first", "last"]
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 27048b82e674c..a7c2aa7c551c5 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -61,10 +61,12 @@
     IndexKeyFunc,
     IndexLabel,
     Level,
+    NaPosition,
     PythonFuncType,
     ReadBuffer,
     Renamer,
     Scalar,
+    SortKind,
     StorageOptions,
     Suffixes,
     TimedeltaConvertibleTypes,
@@ -6426,19 +6428,68 @@ def sort_values(  # type: ignore[override]
         else:
             return result.__finalize__(self, method="sort_values")
 
-    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
+    @overload
+    def sort_index(
+        self,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: Literal[True],
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> None:
+        ...
+
+    @overload
+    def sort_index(
+        self,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: Literal[False] = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> DataFrame:
+        ...
+
+    @overload
     def sort_index(
+        self,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: bool = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> DataFrame | None:
+        ...
+
+    # error: Signature of "sort_index" incompatible with supertype "NDFrame"
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
+    def sort_index(  # type: ignore[override]
         self,
         axis: Axis = 0,
         level: Level | None = None,
-        ascending: bool | int | Sequence[bool | int] = True,
+        ascending: bool | Sequence[bool] = True,
         inplace: bool = False,
-        kind: str = "quicksort",
-        na_position: str = "last",
+        kind: SortKind = "quicksort",
+        na_position: NaPosition = "last",
         sort_remaining: bool = True,
         ignore_index: bool = False,
         key: IndexKeyFunc = None,
-    ):
+    ) -> DataFrame | None:
         """
         Sort object by labels (along an axis).
 
@@ -6529,15 +6580,15 @@ def sort_index(
         d  4
         """
         return super().sort_index(
-            axis,
-            level,
-            ascending,
-            inplace,
-            kind,
-            na_position,
-            sort_remaining,
-            ignore_index,
-            key,
+            axis=axis,
+            level=level,
+            ascending=ascending,
+            inplace=inplace,
+            kind=kind,
+            na_position=na_position,
+            sort_remaining=sort_remaining,
+            ignore_index=ignore_index,
+            key=key,
         )
 
     def value_counts(
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 649cab26d1b9c..d00a2778848ae 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -50,9 +50,11 @@
     JSONSerializable,
     Level,
     Manager,
+    NaPosition,
     NDFrameT,
     RandomState,
     Renamer,
+    SortKind,
     StorageOptions,
     T,
     TimedeltaConvertibleTypes,
@@ -4683,18 +4685,66 @@ def sort_values(
         """
         raise AbstractMethodError(self)
 
+    @overload
     def sort_index(
         self,
-        axis=0,
-        level=None,
-        ascending: bool_t | int | Sequence[bool_t | int] = True,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool_t | Sequence[bool_t] = ...,
+        inplace: Literal[True],
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool_t = ...,
+        ignore_index: bool_t = ...,
+        key: IndexKeyFunc = ...,
+    ) -> None:
+        ...
+
+    @overload
+    def sort_index(
+        self: NDFrameT,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool_t | Sequence[bool_t] = ...,
+        inplace: Literal[False] = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool_t = ...,
+        ignore_index: bool_t = ...,
+        key: IndexKeyFunc = ...,
+    ) -> NDFrameT:
+        ...
+
+    @overload
+    def sort_index(
+        self: NDFrameT,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool_t | Sequence[bool_t] = ...,
+        inplace: bool_t = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool_t = ...,
+        ignore_index: bool_t = ...,
+        key: IndexKeyFunc = ...,
+    ) -> NDFrameT | None:
+        ...
+
+    def sort_index(
+        self: NDFrameT,
+        axis: Axis = 0,
+        level: Level | None = None,
+        ascending: bool_t | Sequence[bool_t] = True,
         inplace: bool_t = False,
-        kind: str = "quicksort",
-        na_position: str = "last",
+        kind: SortKind = "quicksort",
+        na_position: NaPosition = "last",
         sort_remaining: bool_t = True,
         ignore_index: bool_t = False,
         key: IndexKeyFunc = None,
-    ):
+    ) -> NDFrameT | None:
 
         inplace = validate_bool_kwarg(inplace, "inplace")
         axis = self._get_axis_number(axis)
@@ -4715,7 +4765,7 @@ def sort_index(
             if ignore_index:
                 result.index = default_index(len(self))
             if inplace:
-                return
+                return None
             else:
                 return result
 
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 44e8283ff08bb..f53c82972a602 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -39,7 +39,10 @@
     DtypeObj,
     FillnaOptions,
     IndexKeyFunc,
+    Level,
+    NaPosition,
     SingleManager,
+    SortKind,
     StorageOptions,
     TimedeltaConvertibleTypes,
     TimestampConvertibleTypes,
@@ -3575,19 +3578,68 @@ def sort_values(
         else:
             return result.__finalize__(self, method="sort_values")
 
-    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
+    @overload
     def sort_index(
         self,
-        axis=0,
-        level=None,
-        ascending: bool | int | Sequence[bool | int] = True,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: Literal[True],
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> None:
+        ...
+
+    @overload
+    def sort_index(
+        self,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: Literal[False] = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> Series:
+        ...
+
+    @overload
+    def sort_index(
+        self,
+        *,
+        axis: Axis = ...,
+        level: Level | None = ...,
+        ascending: bool | Sequence[bool] = ...,
+        inplace: bool = ...,
+        kind: SortKind = ...,
+        na_position: NaPosition = ...,
+        sort_remaining: bool = ...,
+        ignore_index: bool = ...,
+        key: IndexKeyFunc = ...,
+    ) -> Series | None:
+        ...
+
+    # error: Signature of "sort_index" incompatible with supertype "NDFrame"
+    @deprecate_nonkeyword_arguments(version=None, allowed_args=["self"])
+    def sort_index(  # type: ignore[override]
+        self,
+        axis: Axis = 0,
+        level: Level | None = None,
+        ascending: bool | Sequence[bool] = True,
         inplace: bool = False,
-        kind: str = "quicksort",
-        na_position: str = "last",
+        kind: SortKind = "quicksort",
+        na_position: NaPosition = "last",
         sort_remaining: bool = True,
         ignore_index: bool = False,
         key: IndexKeyFunc = None,
-    ):
+    ) -> Series | None:
         """
         Sort Series by index labels.
 
@@ -3724,15 +3776,15 @@ def sort_index(
         """
 
         return super().sort_index(
-            axis,
-            level,
-            ascending,
-            inplace,
-            kind,
-            na_position,
-            sort_remaining,
-            ignore_index,
-            key,
+            axis=axis,
+            level=level,
+            ascending=ascending,
+            inplace=inplace,
+            kind=kind,
+            na_position=na_position,
+            sort_remaining=sort_remaining,
+            ignore_index=ignore_index,
+            key=key,
         )
 
     def argsort(self, axis=0, kind="quicksort", order=None) -> Series:
diff --git a/pandas/core/sorting.py b/pandas/core/sorting.py
index d41947510c1bb..16facfc915e40 100644
--- a/pandas/core/sorting.py
+++ b/pandas/core/sorting.py
@@ -9,6 +9,7 @@
     Hashable,
     Iterable,
     Sequence,
+    cast,
 )
 import warnings
 
@@ -22,7 +23,10 @@
 from pandas._libs.hashtable import unique_label_indices
 from pandas._typing import (
     IndexKeyFunc,
+    Level,
+    NaPosition,
     Shape,
+    SortKind,
     npt,
 )
 
@@ -47,10 +51,10 @@
 
 def get_indexer_indexer(
     target: Index,
-    level: str | int | list[str] | list[int],
-    ascending: Sequence[bool | int] | bool | int,
-    kind: str,
-    na_position: str,
+    level: Level | list[Level] | None,
+    ascending: Sequence[bool] | bool,
+    kind: SortKind,
+    na_position: NaPosition,
     sort_remaining: bool,
     key: IndexKeyFunc,
 ) -> npt.NDArray[np.intp] | None:
@@ -92,8 +96,12 @@ def get_indexer_indexer(
         ):
             return None
 
+        # ascending can only be a Sequence for MultiIndex
         indexer = nargsort(
-            target, kind=kind, ascending=ascending, na_position=na_position
+            target,
+            kind=kind,
+            ascending=cast(bool, ascending),
+            na_position=na_position,
         )
     return indexer