The child of your nephew is your great nephew (if a son) or your great niece (if a daughter).
Your nephew's daughter is your great niece and you are her great Aunt (or Great Uncle).Correction:Your nephew's daughter is your grand niece. You are her grand aunt or grand uncle.
Your nephew and your daughter are first cousins to each other.Your nephew's son and your daughter are first cousins, once removed, to each other.
Say a woman (let's call her Jane) has a daughter (let's call her Mary) and the daughter (Mary) has a child (let's call the child Carol) Jane is the grandmother of Carol. If Jane has a child other than Mary, that child is Carol's Aunt or Uncle and Carol is that child's Nephew (if Carol is a boy) or Niece (if Carol is a girl). So the relationship between a grandmother's baby and her daughter's baby is that of Aunt/Uncle to Niece/Nephew.
Your child and your great nephew's parents would be first cousins. Their children would then be second cousins. And if they have children, they will be third cousins.
Mother's grandson as regards her daughter is either her (daughter's) son or her (daughter's) nephew.
Your sister's son is your nephew.
Your nephew's son is your great nephew.
Your nephew's daughter's son is your great-great nephew. Your nephew's daughter is your great niece.
Your nephew.
Nephew
A nephew is a cousin to his aunt's son.
Your nephew and grand nephew may be parent and child. In not, then they are First Cousins, Once Removed.
brother
cousins.
niece/nephew
Cousin brother
nephew