The Hindu Goddess Santoshi Mata isn't mentioned clearly in any puranic evidence discovered as of now. But, the question is how do we know so much about the goddess and worship it here like any other goddess?
The first and foremost information we get about the goddess is from the book Santoshi Mata Vrat Katha. The book in detail discusses how the Santoshi Mata's fast is to be observed. The book is the story of a Woman - Satyawati who is mistreated by her family members. She observes fast on 16 consecutive Fridays and the goddess blesses the woman and her wishes are fulfilled.
The book and the goddess find no mentions anywhere before 1960. During this time, a very small section of people from Uttar Pradesh and Bihar began to observe fast and it kept spreading by word of mouth. It was only after the release of the movie titled 'Jai Santoshi Mata' in 1975 the goddess was known throughout India. The wife of Vijay Sharma, the director of the film was also a devotee of the goddess, she encouraged him to spread the word to the masses.
The film was the reason, the goddess Santoshi Mata became so popular and it also fueled feelings of devotion in audiences. The movie explained very little about the origin of the goddess, mentioning her as the daughter of Lord Ganesha. However, the audience who knew very little about the goddess got everything they wished to know about - her Iconography, Magical powers, Fasting Story (Vrat Katha), Impact, Characteristics, the qualities of her ideal devotee, etc. The goddess has certain characteristics of being Benevolent, Gentle, and dependable, she cares for her devotees and rescues them at every peril.
According to some religious scholars the Sri Narada Pancaratra (English edition compiled by Srila Vyasadeva Part 2, Fifth Ratra, Chapter 5, Text 127, page 484)
mentions Santoshi Mata's Characteristics. We still lack conclusive evidence in this regard and could not completely deny or agree if the goddess was puranic or just an example of popular culture in India.