I Like After Tea!

We were sipping tea;
And, I asked her:
“Do you like anything?”
She said: “Yes, after tea!”

I didn't find a clue;
But, there's something behind the blue;
I added the following words,
After 1000 years:

“I've been in my mind lost;
Thoroughly thinking of an algorithm;
At the same time I needed a bit,
From the Shop to buy something,
There were a lot,
Of people ,
In line long;
Staff mentioned with polite:
“Would you like to be in the queue?”
I replied: “I like after Q.”

27 June-10 Aug.