Quis? Ego! (Child's phrase)

Solution 1:

The OED’s earliest citation for this use is from Edith Nesbitt’s ‘The Story of the Treasure Seekers’ in 1899:

‘Any one who likes can have the bottle. Quis?’ And Alice got out ‘Ego’ before the rest of us.

In their classic work ‘Lore and Language of Schoolchildren’, published in 1959, Iona and Peter Opie describe the practice as follows:

In private schools a child who wishes to dispose of something . . . calling out ‘Quis?’ and the boy or girl who first replies ‘Ego’ receives the object and may say (to the horror of the classicist) ‘I egoed it’.

I have no information on the use of ego de to my liking.

Solution 2:

The earliest match I could find for this call and response (in its short form) is from Albert Smith, The Fortunes of the Scattergood Family, serialized in in Bentley's Miscellany, volume 15 (1844):

They [four larger schoolboys at Merchant Tailors] lifted the box on to the table, and then made Frederick who was beginning to cry very piteously, open the lock. The first thing they saw was the accordion, which Mr. Bodle had given him, and which Gogsley directly seized on, holding up at arms' length, and shouting out,

"Quis?"

"Ego!" cried the other three all at once.

"Yours, Plunkett," he exclaimed, handing it over to a genteel-looking youth, in broad lay-down collars, who directly commenced a very rapid fantasia upon it, introducing no particular air, which terminated in putting several of the notes entire hors de combat.

And likewise from "The Little Handful of Thorns," in The Sunday at Home: A Family Magazine for Sabbath (1875):

A summer day ; earnestly hot. Never mind, it is necessary for the rector to go to Chee-combe (a little hamlet in his parish) to see old Thomas Warne. "Who will go with me? Quis?" "Ego!" shouts the youngest girl, an exceeding fatling of three years old (precociously imitating her brother's Latin, to his delight). " No, not you, my pet ; the stout, sturdy legs are not equal to a walk over these hills ; not yet, at least. But Siward and Elgiva, they, if they like may come with father."

Eric Partridge, A Dictionary of Slang and Unconventional English, second edition (1938) has this entry for the expression:

quis? Who wants some? : Public-Schoolboys' : mid-C. 19–20. The answer is ego! [W.E.] Collinson [Contemporary English (1927)]. Direct ex Latin.

It thus appears that the schoolboy call and response of "Quis?" "Ego!" antedates by at least 55 years the earliest OED citation noted in Barrie England's answer. Like Barrie England, I could not find any trace of "Quis?" "Ego de to my liking."

Solution 3:

I went to a (very British type of) private Anglican school in South Africa in the 70's, and recall the 'quis? ego' quite vividly. It generally had to do when someone had too much of something (eg. Fruit that was soon to get over ripe) and was willing to give it away. The first to say 'ego' generally got it, but there were often squabbles about who was really first. Never heard a teacher do it. Never heard a formal rule about it, you just sort of learnt it. The only trick or variant I knew was when someone would want to tease or provoke someone else, they would take something of theirs (eg. A pen) right from under their nose and 'quis, ego' it away and let the person whose article had been taken away to sort out the ensuiing chaos and arguments.