他 有 几 个 孩子

(a) and (b) are correct. However, "一些" is generally used to mean "some" instead of "several". "Several" seems more in quantity than "some". I would prefer to say "several" as "好几个" but "一些" would not be considered wrong. (c) is a bit vague because 孩子 alone can mean "child" or "children". But overall, it is best to state exactly how many children he has. e.g. 他有两个孩子

他有几个孩子

if you have to choose one,b will be the only one that can be chosen .But usually we don't say anything like that. We will say 他有几个孩子 .Cherry said several should be as 好几个.It's not right,for in Chinese 好几个 contains the meaning of ‘many’ to some extend.C means he has got at least one child,so it's wrong. And A actually is totally wrong,we will never say this sentence.有些 has many usages,but it can't be used here.You will master these usages automatically little by little if you keep learning Chinese.Wish you success!

a and b are the same, but we don't usually say “些/一些孩子”, and we say "几个孩子"。 so the most correct answer is 他有几个孩子。