Verb used to deny age
Yes, we use 不是 and 没有, for different meaning.

我不是二十岁。  
I'm not twenty years old. (Probably 10, or 30, ...)

我没有二十岁。
I'm less than twenty years old.


PS: You could use 是 such as 我是二十岁 to emphasize the fact (that you're twenty). And when asked with the specified age, we usually answer it with using 是. e.g.

你是二十岁吗？
我是二十岁。


When asked about the age generally, we usually answer it without using 是.

你多大？
我二十岁。