In Greek mythology, Athena is often said to be favourite child of Zeus. The only proof that I know of is him gifting her his shield (Aegis).
But are there any other myths that provide proof for this claim?
In the Iliad (Book V) Ares complains to Zeus that he lets Athena - the pestilent maiden - get away with anything:
Speedily he came to the abode of the gods, to steep Olympus, and sate him down by the side of Zeus, son of Cronos, grieved at heart, and shewed the immortal blood flowing from the wound, and with wailing spake to him winged words:
“Father Zeus, hast thou no indignation to behold these violent deeds? Ever do we gods continually suffer most cruelly by one another's devices, whenas we show favour to men. With thee are we all at strife, for thou art father to that mad and baneful maid, whose mind is ever set on deeds of lawlessness. For all the other gods that are in Olympus are obedient unto thee, and subject to thee, each one of us; but to her thou payest no heed whether in word or in deed, but rather settest her on, for that this pestilent maiden is thine own child. Now hath she set on the son of Tydeus, Diomedes high of heart, to vent his rage upon immortal gods. Cypris first he wounded with a thrust in close fight upon the hand at the wrist, and thereafter rushed upon mine own self as he had been a god. Howbeit my swift feet bare me away; otherwise had I long suffered woes there amid the gruesome heaps of the dead, or else had lived strengthless by reason of the smitings of the spear.”
This is in response to Athena helping her favorite Diomedes wound Ares in battle.