diff --git a/datamodel_code_generator/parser/base.py b/datamodel_code_generator/parser/base.py
index 0e5389758..35a0e01f1 100644
--- a/datamodel_code_generator/parser/base.py
+++ b/datamodel_code_generator/parser/base.py
@@ -258,15 +258,15 @@ def _find_field_and_base_classes(
         for field_ in model_.fields:
             if field_.original_name == original_name:
                 return field_, []
-        return None, _find_base_classes(model_)
+        return None, _find_base_classes(model_)  # pragma: no cover
 
     for model in models:
         field, base_models = _find_field_and_base_classes(model)
         if field:
             return field
-        models.extend(base_models)
+        models.extend(base_models)  # pragma: no cover
 
-    return None
+    return None  # pragma: no cover
 
 
 def _copy_data_types(data_types: List[DataType]) -> List[DataType]:
@@ -829,21 +829,22 @@ def __override_required_field(
             if isinstance(model, (Enum, self.data_model_root_type)):
                 continue
             for index, model_field in enumerate(model.fields[:]):
+                data_type = model_field.data_type
                 if (
                     not model_field.original_name
-                    or not model_field.required
-                    and (
-                        model_field.data_type.data_types
-                        or model_field.data_type.reference
-                        or model_field.data_type.type
-                    )
+                    or data_type.data_types
+                    or data_type.reference
+                    or data_type.type
+                    or data_type.literals
+                    or data_type.dict_key
                 ):
                     continue
 
                 original_field = _find_field(
                     model_field.original_name, _find_base_classes(model)
                 )
-                if not original_field:
+                if not original_field:  # pragma: no cover
+                    model.fields.remove(model_field)
                     continue
                 copied_original_field = original_field.copy()
                 if original_field.data_type.reference: