afteryoudaoicibaDictYouDict[after 词源字典]
after: [OE] In the first millennium AD many Germanic languages had forms cognate with Old English æfter (Gothic aftra, for example, and Old Norse aptr), but, with the exception of Dutch achter, none survive. It is not clear what their ultimate origin is, but the suffix they share may well be a comparative one, and it is possible that they derive from a Germanic base *af- (represented in Old English æftan ‘from behind’).

It has been suggested that this goes back to Indo-European *ap- (source of Latin ab ‘away, from’ and English of(f)), in which case after would mean literally ‘more off’ – that is, ‘further away’. Nautical aft is probably a shortening of abaft, formed, with the prefixes a- ‘on’ and be- ‘by’, from Old English æftan.
=> of, off[after etymology, after origin, 英语词源]
after (prep.)youdaoicibaDictYouDict
Old English æfter "after, next, throughout, following in time, later," from Old English of "off" (see of) + -ter, a comparative suffix; thus the original meaning was "more away, farther off." Compare Old Norse eptir "after," Old High German aftar, Gothic aftra "behind." Cognate with Greek apotero "farther off."

After hours "after regular working hours" is from 1861. Afterwit "wisdom that comes too late" is attested from c. 1500 but seems to have fallen from use, despite being more needed now than ever. After you as an expression in yielding precedence is recorded by 1650.