She is a disciple of Shiva but not his daughter.
She is said to be the mind born daughter of Sage Kashyapa in Devi Bhagavatam 9.47:
38-58. Nârâyana said :-- O Nârada! Thus I narrated to you the stories
of Sasthî and Mangala Chandîkâ, according to the Vedas. Now hear the
story of Manasâ that I heard from the mouth of Dharama Deva.
Manasâ is the mind-born daughter of Maharsi Kas’yapa; hence she is named Manasâ; or it may be She who plays with the mind is Manasâ. Or
it may be She who meditates on God with her mind and gets rapture in
Her meditation of God is named Manasâ. She finds pleasure in Her Own
Self, the great devotee of Visnu, a Siddha Yoginî. For three Yugas She
worshipped S’rî Krisna and then She became a Siddha Yoginî. S’rî
Krisna, the Lord of the Gopîs, seeing the body of Manasâ lean and thin
due to austerities, or seeing her worn out like the Muni Jarat Kâru
called her by the name of Jarat Kâru. Hence Her name has come also to
be Jarat Kâru. Krisna, the Ocean of Mercy, gave her out of kindness,
Her desired boon; She worshipped Him and S’rî Krisna also worshipped
Her. Devî Manasâ is known in the Heavens, in the abode of the Nâgas
(serpents), in earth, in Brahmâloka, in all the worlds as of very fair
colour, beautiful and charming. She is named Jagad Gaurî as she is of
a very fair colour in the world. Her other name is S’aivî and she is
the disciple of S’iva. She is named Vaisnavî as she is greatly devoted
to Visnu. She saved the Nâgas in the Snake Sacrifice performed by
Pariksit, she is named Nages’varî and Nâga Bhaginî and She is capable
to destroy the effects of poison. She is called Visahari.