Fidius
An ancient form of filius, occurs in the connection of Dius Fidius, or Medius fidius, that is, me Dius filius, or the son of Zeus, that is, Hercules. Hence the expression medius fidius is equivalent to me Hercules, scil. juvet. (Cic. ad Fam. v. 21; Plin. Epist. iv. 3.) Sometimes Fidius is used alone in the sense of the son of Zeus or Hercules. (Fasti By Ovid vi. 213; comp. Varro, de L. L. v. 66; Plaut. Asin. i. 1. 8; Varro, ap. Non. viii. 93.) Some of the ancients connected fidius with fides. (Festus s. v. medius.)
From Smith's Dictionary of Greek and Roman Biography and MythologyFrom Fasti By Ovid Book VI: June 5: Nones
I asked whether I should assign the Nones to Sancus,
Or Fidius, or you Father Semo: Sancus answered me:
'Whichever you assign it to, the honour's mine:
I bear all three names: so Cures willed it.'
The Sabines of old granted him a shrine accordingly,
And established it on the Quirinal Hill.