Is there any story, about born on opposite sex?
Yes, there is a story of King Puranjana in Shreemad Bhagvat purana, where the King Puranjana was reborn as women- SB 4.28 : Purañjana Becomes a woman in the next Life.
This is an ancient story told by Narada to king Prachinbarhi.
Background - This is a story of King Puranjana who was engaged in sense gratification throughout his life. Unkind king, Purañjana, had killed many animals in various sacrifices. Now, taking advantage of this opportunity, all these animals began to pierce him with their horns. Due to his contaminated association with women King Purañjana suffered very much and lost his kingdom.And at the end he died remembering his wife , so he was reborn as a women.
Now it is believed that whatever a man constantly thinks in his death bed or while dying, he gets rebirth according to his last thoughts.
So king Puranjana died thinking of his wife and reborn as a woman.
तामेव मनसा गृह्यन बभूव प्रमदोत्तमा ।
अनन्तरं विदर्भस्य राजसिंहस्य वेश्मनि ।।28।।
tām eva manasā gṛhṇan babhūva pramadottamā
anantaraṁ vidarbhasya rāja-siṁhasya veśmani
King Purañjana gave up his body while remembering his wife, and consequently in his next life he became a very beautiful and
well-situated woman. He took his next birth as the daughter of King
Vidarbha in the very house of the King.SB 4.28.28