diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index f494e74bde55f..8d8a62a58f25f 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -363,8 +363,8 @@ def format_array_from_datetime(
 
 def array_with_unit_to_datetime(
     ndarray values,
-    object unit,
-    str errors='coerce'
+    str unit,
+    str errors="coerce"
 ):
     """
     Convert the ndarray to datetime according to the time unit.
@@ -384,7 +384,7 @@ def array_with_unit_to_datetime(
     ----------
     values : ndarray of object
          Date-like objects to convert.
-    unit : object
+    unit : str
          Time unit to use during conversion.
     errors : str, default 'raise'
          Error behavior when parsing.
diff --git a/pandas/_libs/tslibs/conversion.pxd b/pandas/_libs/tslibs/conversion.pxd
index 2cf75944a8196..0eb94fecf7d6b 100644
--- a/pandas/_libs/tslibs/conversion.pxd
+++ b/pandas/_libs/tslibs/conversion.pxd
@@ -13,7 +13,7 @@ cdef class _TSObject:
         bint fold
 
 
-cdef convert_to_tsobject(object ts, tzinfo tz, object unit,
+cdef convert_to_tsobject(object ts, tzinfo tz, str unit,
                          bint dayfirst, bint yearfirst,
                          int32_t nanos=*)
 
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 95500f66db156..a1f074b1b29a8 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -56,8 +56,19 @@ TD64NS_DTYPE = np.dtype('m8[ns]')
 # Unit Conversion Helpers
 
 cdef inline int64_t cast_from_unit(object ts, str unit) except? -1:
-    """ return a casting of the unit represented to nanoseconds
-        round the fractional part of a float to our precision, p """
+    """
+    Return a casting of the unit represented to nanoseconds
+    round the fractional part of a float to our precision, p.
+
+    Parameters
+    ----------
+    ts : int, float, or None
+    unit : str
+
+    Returns
+    -------
+    int64_t
+    """
     cdef:
         int64_t m
         int p
@@ -307,7 +318,7 @@ cdef class _TSObject:
         return self.value
 
 
-cdef convert_to_tsobject(object ts, tzinfo tz, object unit,
+cdef convert_to_tsobject(object ts, tzinfo tz, str unit,
                          bint dayfirst, bint yearfirst, int32_t nanos=0):
     """
     Extract datetime and int64 from any of:
@@ -497,7 +508,7 @@ cdef _TSObject _create_tsobject_tz_using_offset(npy_datetimestruct dts,
     return obj
 
 
-cdef _TSObject _convert_str_to_tsobject(object ts, tzinfo tz, object unit,
+cdef _TSObject _convert_str_to_tsobject(object ts, tzinfo tz, str unit,
                                         bint dayfirst=False,
                                         bint yearfirst=False):
     """
@@ -513,6 +524,7 @@ cdef _TSObject _convert_str_to_tsobject(object ts, tzinfo tz, object unit,
         Value to be converted to _TSObject
     tz : tzinfo or None
         timezone for the timezone-aware output
+    unit : str or None
     dayfirst : bool, default False
         When parsing an ambiguous date string, interpret e.g. "3/4/1975" as
         April 3, as opposed to the standard US interpretation March 4.
diff --git a/pandas/_libs/tslibs/timedeltas.pxd b/pandas/_libs/tslibs/timedeltas.pxd
index 70a418d7803d1..4142861e9ad38 100644
--- a/pandas/_libs/tslibs/timedeltas.pxd
+++ b/pandas/_libs/tslibs/timedeltas.pxd
@@ -3,7 +3,7 @@ from numpy cimport int64_t
 
 # Exposed for tslib, not intended for outside use.
 cpdef int64_t delta_to_nanoseconds(delta) except? -1
-cdef convert_to_timedelta64(object ts, object unit)
+cdef convert_to_timedelta64(object ts, str unit)
 cdef bint is_any_td_scalar(object obj)
 
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 2862e62e3d522..8f3a599bf107c 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -160,7 +160,7 @@ cpdef int64_t delta_to_nanoseconds(delta) except? -1:
     raise TypeError(type(delta))
 
 
-cdef convert_to_timedelta64(object ts, object unit):
+cdef convert_to_timedelta64(object ts, str unit):
     """
     Convert an incoming object to a timedelta64 if possible.
     Before calling, unit must be standardized to avoid repeated unit conversion
@@ -218,7 +218,7 @@ cdef convert_to_timedelta64(object ts, object unit):
 
 @cython.boundscheck(False)
 @cython.wraparound(False)
-def array_to_timedelta64(object[:] values, unit=None, errors='raise'):
+def array_to_timedelta64(object[:] values, str unit=None, str errors="raise"):
     """
     Convert an ndarray to an array of timedeltas. If errors == 'coerce',
     coerce non-convertible objects to NaT. Otherwise, raise.
@@ -470,7 +470,7 @@ cdef inline timedelta_from_spec(object number, object frac, object unit):
     return cast_from_unit(float(n), unit)
 
 
-cpdef inline str parse_timedelta_unit(object unit):
+cpdef inline str parse_timedelta_unit(str unit):
     """
     Parameters
     ----------
diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index e104b722ea119..b79a5c49bdd10 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -1050,6 +1050,7 @@ class Timestamp(_Timestamp):
             nanosecond = hour
             tz = minute
             freq = None
+            unit = None
 
         if getattr(ts_input, 'tzinfo', None) is not None and tz is not None:
             raise ValueError("Cannot pass a datetime or Timestamp with tzinfo with "