diff --git a/src/ytdl_sub/script/parser.py b/src/ytdl_sub/script/parser.py
index ac6260ff..3fa53a75 100644
--- a/src/ytdl_sub/script/parser.py
+++ b/src/ytdl_sub/script/parser.py
@@ -25,13 +25,12 @@ from ytdl_sub.script.utils.exceptions import UNREACHABLE
 from ytdl_sub.script.utils.exceptions import CycleDetected
 from ytdl_sub.script.utils.exceptions import FunctionDoesNotExist
 from ytdl_sub.script.utils.exceptions import IncompatibleFunctionArguments
+from ytdl_sub.script.utils.exceptions import InvalidCustomFunctionArgumentName
 from ytdl_sub.script.utils.exceptions import InvalidSyntaxException
 from ytdl_sub.script.utils.exceptions import InvalidVariableName
 from ytdl_sub.script.utils.exceptions import UserException
 from ytdl_sub.script.utils.exceptions import VariableDoesNotExist
 from ytdl_sub.script.utils.name_validation import validate_variable_name
-from ytdl_sub.utils.exceptions import StringFormattingException
-from ytdl_sub.validators.string_formatter_validators import is_valid_source_variable_name
 
 # pylint: disable=invalid-name
 # pylint: disable=too-many-branches
@@ -197,6 +196,7 @@ class _Parser:
         Begin parsing function args after the first ``$``, i.e. ``$0``
         """
         var_name = ""
+        variable_start_pos = self._pos
         while ch := self._read(increment_pos=False):
             if ch.isspace() and not var_name:
                 self._pos += 1
@@ -204,15 +204,14 @@ class _Parser:
             if _is_breakable(ch):
                 break
 
-            is_numeric = ch.isnumeric()
-            if not is_numeric:
-                raise StringFormattingException("invalid function var name")
-
             var_name += ch
             self._pos += 1
 
-        if not var_name:
-            raise StringFormattingException("invalid var name")
+        if not var_name.isnumeric():
+            self._set_highlight_position(variable_start_pos)
+            raise InvalidCustomFunctionArgumentName(
+                "Custom function arguments must be numeric and increment starting from zero."
+            )
 
         return FunctionArgument.from_idx(idx=int(var_name), custom_function_name=self._name)
 
diff --git a/src/ytdl_sub/script/utils/exceptions.py b/src/ytdl_sub/script/utils/exceptions.py
index f24a382d..fa67e1f0 100644
--- a/src/ytdl_sub/script/utils/exceptions.py
+++ b/src/ytdl_sub/script/utils/exceptions.py
@@ -19,6 +19,10 @@ class InvalidFunctionName(UserException):
     """Custom function name is invalid"""
 
 
+class InvalidCustomFunctionArgumentName(UserException):
+    """Custom function argument name (i.e. $0) is invalid"""
+
+
 class IncompatibleFunctionArguments(UserException):
     """Function has invalid arguments"""
 
diff --git a/tests/unit/script/types/test_custom_function.py b/tests/unit/script/types/test_custom_function.py
index 2c9d2692..01708f98 100644
--- a/tests/unit/script/types/test_custom_function.py
+++ b/tests/unit/script/types/test_custom_function.py
@@ -7,6 +7,7 @@ from ytdl_sub.script.types.array import ResolvedArray
 from ytdl_sub.script.types.resolvable import Integer
 from ytdl_sub.script.utils.exceptions import CycleDetected
 from ytdl_sub.script.utils.exceptions import FunctionDoesNotExist
+from ytdl_sub.script.utils.exceptions import InvalidCustomFunctionArgumentName
 
 
 class TestCustomFunction:
@@ -80,3 +81,26 @@ class TestCustomFunction:
                     "output": "{%func(1)}",
                 }
             ).resolve()
+
+    @pytest.mark.parametrize(
+        "name",
+        [
+            "$00invalid",
+            "$abc",
+            "$3.14",
+        ],
+    )
+    def test_custom_function_invalid_function_arguments(self, name: str):
+        with pytest.raises(
+            InvalidCustomFunctionArgumentName,
+            match=re.escape(
+                "Custom function arguments must be numeric and increment starting from zero."
+            ),
+        ):
+            Script(
+                {
+                    "%func1": f"{{%mul(1, {name})}}",
+                    "%func0": "{%mul(%func1(1), $0)}",
+                    "output": "{%func0(1)}",
+                }
+            ).resolve()
diff --git a/tests/unit/script/types/test_float.py b/tests/unit/script/types/test_float.py
index 104a38a8..1328c5b1 100644
--- a/tests/unit/script/types/test_float.py
+++ b/tests/unit/script/types/test_float.py
@@ -25,7 +25,7 @@ class TestFloat:
     )
     def test_float_not_arg(self, integer: str):
         with pytest.raises(InvalidSyntaxException, match=re.escape(str(NUMERICS_ONLY_ARGS))):
-            Script({"float": integer}).resolve()
+            Script({"out": integer}).resolve()
 
     @pytest.mark.parametrize(
         "float_, expected_float",
@@ -57,7 +57,7 @@ class TestFloat:
     )
     def test_invalid_float(self, float_: str):
         with pytest.raises(InvalidSyntaxException, match=re.escape(str(NUMERICS_INVALID_CHAR))):
-            Script({"float": float_}).resolve()
+            Script({"out": float_}).resolve()
 
     @pytest.mark.parametrize(
         "to_cast, expected_float",
diff --git a/tests/unit/script/types/test_string.py b/tests/unit/script/types/test_string.py
index 1a40229b..6fc990ba 100644
--- a/tests/unit/script/types/test_string.py
+++ b/tests/unit/script/types/test_string.py
@@ -23,7 +23,7 @@ class TestString:
     )
     def test_string_not_arg(self, string: str):
         with pytest.raises(InvalidSyntaxException, match=re.escape(str(STRINGS_ONLY_ARGS))):
-            Script({"string": string}).resolve()
+            Script({"out": string}).resolve()
 
     @pytest.mark.parametrize(
         "string, expected_string",
@@ -59,4 +59,4 @@ class TestString:
     )
     def test_string_not_closed_properly(self, string: str):
         with pytest.raises(InvalidSyntaxException, match=re.escape(str(STRINGS_NOT_CLOSED))):
-            Script({"string": string}).resolve()
+            Script({"out": string}).resolve()