Yes, their were cousins.
Mordecai is the one cousin whose name is recorded.See also:More about Esther and Mordecai
Esther was raised by her cousin Mordecai.
Mordecai reminds queen Esther that if she keeps quiet and does not go to the king, vengence will come from somewhere else.
Esther was Mordecai's uncle's daughter. Esther 2:7 And he brought up Hadassah, that is, Esther, his uncle's daughter: for she had neither father nor mother, and the maid was fair and beautiful; whom Mordecai, when her father and mother were dead, took for his own daughter.
Mordecai
She was an orphan. but his name was Abihail Her mother is not mentioned Esther was adopted by her cousin, Mordecai.(Esther 2:5-7)
The Bible does not say who her father was. Her uncle's name was Mordecai.
Hatach was the messenger between Mordecai and Esther. Vashti was the Queen whose reign was given to Esther. Ahaseurus (who is traditionally identical with Xerxes) made Esther his Queen.
Mordecai was Esther's cousin.See also:More about Esther
Mordecai, one of the Jews exiled to Babylonia after the First Destruction, was the cousin of Queen Esther. He was one of the leading Jewish sages of the time. His deeds are recounted at length in the Book of Esther (and are too many to list here). By the end of the reign of King Ahaseurus, Mordecai had become viceroy to the King.
Esther was an Israelite from Judea (Israel). Mordecai, Esther's cousin, came from the tribe of Benjamin (Esther 2:5). While not directly mentioned, it can be inferred from this that Esther was also from the tribe of Benjamin.
Esther was a young Jewish woman who became the queen of Persia. She was raised by her cousin Mordecai who was a minor official at the palace of Xerxes the Persian King. Xerxes divorced his wife and chose Esther to be the new queen.