Your niece.
Your brother's daughter would be your niece and you'd be her uncle or aunt. Your sister's daughter would also be your niece. If your sibling had a son, he would be your nephew.
You would call the daughter of your brother a niece.
Your brother's (or sister's) daughter is your niece.
The daughter of your brother or sister is your niece.
Your niece, of course!
niece
Niece
Your brother's sister is your daughter's aunt, and your daughter is your brother's, and his sister's, niece.
Your brother or sister's daughter is called 'your niece.'
Your sister's daughter and your sister's brother are niece and uncle to each other. The daughter is the niece of the brother and the brother is uncle to the daughter.
If your brother-in-law is your spouse's brother, then his sister's daughter is your spouse's niece, and your niece, too. If your brother-in-law is your sister's husband, then his sister is not related to you, and neither is her daughter.
You brother's daughter is your niece, just as your sister's daughter is your niece. The English language does not have different terms for daughter of brother and sister.
I guess you will be her uncle. Consider this case.. You have a brother and he has a daughter.. Your daughter will be a sister in law to your brother's daughter.
Your brother or sister's daughter is your niece.
Your sister's husband is your brother-in-law. The daughter of his sister is his niece, and your sister's niece, but is not related to you. Assuming the child was born to the woman before she met your brother, the daughter of the woman whose brother married your sister is not related to you.
If you are female, your sister's brother-in-law could be your husband. Then his daughter is either your daughter or your step daughter. Your sister's brother-in-law could also be the husband of another sister. Then her daughter would be your niece. Otherwise, there is no relationship as you do not share a common ancestor.
If your brother-in-law is the husband of your sister, presumably his daughter is your sister's daughter, too. Then his daughter and your nephew are either brother and sister or first cousins. If the daughter is not your sister's daughter, but the child of a previous marriage, then she is could be the half-sister of your nephew or not related to your nephew at all. If your brother-in-law is the brother of your spouse, then his daughter is your niece and your niece and your nephew are either siblings, first cousins, or not related at all, depending on how your nephew is related to you.
If your sister-in-law is your spouse's sister, her brother is your spouse's brother and therefore is your brother-in-law, or perhaps your husband. If your sister-in-law is the wife of your brother, her brother is your brother's brother-in-law but is not related to you. The English language has no relationship term for the brother of your sibling's spouse.
sister