I was wondering if a child got refused from canada or any other country as a part of parent short stay visa application-(refused as a part of his or her family's visa Application, then whether it in future while applying for any other country like Uk,US she or she would have to mentioned it or not? More specifically, Either the family's refusal is also considered His/her- previous refusal or not and either he/she is supposed to mention while applying in any other country's short stay visa application or not? considering gonna travel alone for short stay study visa and is still minor 12 or 13?
Yes, it absolutely needs to be answered in Yes if a form ever asks if a visa was ever refused. Unless the child doesn’t remember or was never told by you, that would be a genuine reason. If you deliberately hide it thinking your child was too young back then then that is deception.
There is no such thing as family's refusal. All children for most countries apply on their own form as a dependent of the main applicant and the decision is tied to their own history. They will obviously give weight to the fact that at the time of that refusal the applicant was a minor and completely dependent on the family so it is not a show-stopper.
It was a refusal without a doubt. Whether you say No and get away with it is a subjective thing and no one can answer that definitely.