W.B. Stanford writes in relation to ἄττα in Odyssey 16.31:
'Doubtless a vestige of baby-talk like πάππα... and μαῖα...; cp. μάμμη, τατᾶ, τατί, ἄππα, τίτθη in L-S-J. The doubling of a consonant or syllable... is typical of this kind of word: 'Mummy', 'Daddy', 'gee-gee', 'puff-puff', 'Nana'. If there were a masculine form of the last it would be the aptest translation here. 'Old fellow' in the friendly sense approximates to the tone, but not the form, of the word. Perhaps 'Gaffer' is the nearest English equivalent.'
'Gaffer' is thought to be a contraction of 'Godfather'.