diff --git a/fsspec/implementations/reference.py b/fsspec/implementations/reference.py
index c14ee8302..cf88304ee 100644
--- a/fsspec/implementations/reference.py
+++ b/fsspec/implementations/reference.py
@@ -41,7 +41,7 @@ def _first(d):
 
 def _prot_in_references(path, references):
     ref = references.get(path)
-    if isinstance(ref, (list, tuple)):
+    if isinstance(ref, (list, tuple)) and isinstance(ref[0], str):
         return split_protocol(ref[0])[0] if ref[0] else ref[0]
 
 
@@ -845,6 +845,9 @@ def cat(self, path, recursive=False, on_error="raise", **kwargs):
                 # found and on_error is "raise"
                 try:
                     u, s, e = self._cat_common(p)
+                    if not isinstance(u, (bytes, str)):
+                        # nan/None from parquet
+                        continue
                 except FileNotFoundError as err:
                     if on_error == "raise":
                         raise
diff --git a/fsspec/mapping.py b/fsspec/mapping.py
index 8fb9b9efb..752eef352 100644
--- a/fsspec/mapping.py
+++ b/fsspec/mapping.py
@@ -112,7 +112,7 @@ def getitems(self, keys, on_error="raise"):
             for k, v in out.items()
         }
         return {
-            key: out[k2]
+            key: out[k2] if on_error == "raise" else out.get(k2, KeyError(k2))
             for key, k2 in zip(keys, keys2)
             if on_error == "return" or not isinstance(out[k2], BaseException)
         }