Who is the daughter of lord Shiva?

Lord Shiva having a daughter is only mentioned in Padma Purana. Once Lord Shiva was explaining about the powers of Kalpavriksha to goddess Parvati. Kalpavriksha tree has powers to bestow anything a person desires. Goddess Parvati desired a daughter and a girl child was obtained from Kalpavriksha.

The goddess heard the wonderful words of Śiva. With his consent, she mentally conceived a very virtuous and beautiful gem of a body. The Daughter of the Mountain obtained from that great tree a woman who was (so) lovely in all limbs, virtuous and beautiful that she, helping Cupid, had come to delude the universe.

Source: Padma Purana Bhumi Kanda chapter 102

Goddess Parvati named her Ashoksundari and further told her daughter that Nahusha will become her husband in the near future.

Śrī Devī (i.e. Pārvatī) said:

Through curiosity about the truth about the tree, I conceived you. O good lady, the fruit, i.e. you, the wealth of beauty is instantly obtained. You are undoubtedly my daughter endowed with all good fortune. You will be known in the world as Aśokasundarī. Nahuṣa, lord of kings, well known in the lunar family, like god Indra, will be your husband.

Source: Padma Purana Bhumi Kanda chapter 102

The above story does not have any cross references in any other scripture. In fact it contradicts other scriptures like Harivamsha. According to Harivamsha, Nahusha’s wife was Viraja.

• The ancestral manes of the Patriarch Karddama, Sudhanwās by name, came into being from the noble Brahmana Pulaha (64).
• They, gifted with etherial movements, are living in the regions where the dwellers move about of their own will. The Vaishyas who wish to reap the fruits of their actions, offer oblations unto them (65).
• Their mind-born daughter is celebrated by the name of Viraja. O Brahman, she will be the mother of Yayati and the wife of Nahusha.

Source: Harivamsha Chapter 18

Viraja is directly mentioned as mind born daughter of the Pitrus and therefore Ashoksundari and Viraja are not the same person. Therefore it is possible to conclude that story of Ashoksundari may be interpolation and later added.