There aren’t enough texts and documents regarding Chandragupta Maurya, this is the reason why there are several assumption and speculations about his personal life.
While, his family tree is widely known, there are questions whether he had a sister or not.
Did Chandragupta Maurya Had a Sister?
It is known that Chandragupta stayed with his foster parents. There are chances that he might have a sister either from the foster parents or his real parents but nothing has been documented well to prove that.
Perhaps, he might have a sister but since the available texts focuses more on his power and struggle, it would have simply ignored to focus on his siblings.
Then there are chances that he might have no sister or brother, and this is the reason why there is no mention about them.
Then Who is Chhaya in Chandra Nandni?
Chandra Nandni is basically a fictional show. So, Chhaya is a fictional or you can say a questionable character. Now since she has no historical connection, the writers can craft anything based on their imagination.
So, Chhaya staying in Vaishali, having an affair with goldsmith and then trying to meet her lover is nothing but an internal formulated story of this historical fiction.
There is no evidence or supporting documents that prove Chandragupta Maurya had a sister. And even if he had, there is no connection (in terms of life story) between the real sister and the one shown in the serial Chandra Nandini.