Your father's niece is your first cousin, and her daughter is your first cousin, once removed.
Your first cousin's niece is the daughter of her brother or sister. Your first cousin's brothers and sisters are also your first cousins. So your first cousin's niece is the daughter of your first cousin and is therefore your first cousin, once removed.
A niece. How could you not know that
Your mother's niece is your first cousin. Your first cousin's daughter is your first cousin, once removed.
Either they are second cousins or technically not related at all. Your cousin's niece would be one of her siblings' children, in which case it would one of your cousin's daughters, or her spouses' niece, in which case there is no blood relationship, but most families would refer to them as a cousin.
Your Dad's niece is your first cousin. Their child would be your first cousin once removed.
Your grandfather's first cousin is your first cousin twice removed. You are both descended from one of your great great great grandparents. His wife, however is not related to you.Her niece might be the daughter of a sibling of your grandfather's first cousin. (Remember that your aunt can be the wife of your parent's brother or the sister of your parent.) In that case, the niece is your first cousin once removed.The other possibility is that the niece is the daughter of the sibling of the first cousin's wife. Since the wife is not related to you, her sibling would not be related t you and the wife's niece is not related to you at all.
Since your niece is your daughter's first cousin, your grand niece (the daughter of your niece) is your daughter's first cousin, once removed.
Your niece is the first cousin of your children and the first cousin, once removed, of your grandchildren.
Your father's niece is your first cousin, and her daughter is your first cousin, once removed.
Your grandfather's niece is the first cousin to one of your parents. That would make you first cousins once removed. Most families just use the term cousin.
There is no actual blood relationship. If this was your mother's niece, it would be your first cousin. In most families, she would be referred to as a cousin, even without the blood connection.