A noun in The Etymologies of the 1930s glossed “small bird” derived from the root ᴹ√PHILIK and cognate to ᴹQ. filit (filik-) of the same meaning (Ety/PHILIK). Tolkien said fileg was an “analogical singular” form (along with another singular form filigod) based on its plural form filig. That is because the final -k in ✱philik was lost in ancient times, as explained in Common Eldarin: Noun Structure from the early 1950s (PE21/72) so that its historical phonetic development would have produced singular N./S. ✱fil. This form was deemed unsuitable, and a new singular form fileg was constructed based on the plural. Something similar happened with S. thoron “eagle”.
Neo-Sindarin: I think it is likely that fileg can also be used to refer to sparrows for purposes of Neo-Sindarin, since its Quenya cognate filit was in one place glossed “sparrow, small bird” (PE21/56).