(Exercise in English coursebook, suggesting that the correct answer is "I had a hamster when I was little").
Answers:
Actually, GOT is incorrect English. I was taught this at school many years ago.
We use GOT as a past participle of the verb to GET. It actually should be GOTTEN, but who says 'gotten' these days!!??
It is used to put stress on statements such as " I have GOT TO have it!!" The correct way to say that would be "I HAVE to have it."
or, "I MUST have it."
It is very often unnecessary. . .In your example it is totally unnecessary.
If you were referring to the fact you POSSESSED a hamster,
you would just say "I had a hamster....".
If you were talking about acquiring a hamster, you would say: "I had bought," or, "I had been given".. . . . "Got" is not needed.