‘Uchchhishta Ganapti Worship is shrouded in mystery.
Ganapati, meaning head of the Shiva Ganas which includes Nandi , Chandikeswara and Veerabhadra is traditionally worshiped as the embodiment of Pranava , OM.
He is venerated in such a way there is an Upnishad dedicated to Him.
Please read my article on this.
There are 32 forms of Ganapati.
One of them is Uchchishta Ganapati.
This form of worship is believed to be a form of Vamachara(left handed worship), meaning Black magic worship)
Description of the worship is provided in this article.
This practice is attributed to Tantra Sastra.
In Sanskrit Vama means ‘left’
Shakti occupies the left portion of Shiva.
The form of Shiva is Universe in Motion.
Look at Nataraja.
He represents Sruthi and Laya.
Movement with harmony Uniformity(sruthi) and Rhythm(laya)
Those who know music can tell you that sruthi and laya are described thus
When these combine Uniform Motion is set.
In Music , sound becomes Music.
Now Devi occupies the left portion of Shiva.
Shiva is Inert(Jata) Potential Energy.
Shakti is Kinetic Energy , the Soul.
One is ineffective without the other.
Each complements the other.
Kalidasa describes Shiva and Parvati as word and meaning.
So does Abhirami Bhattar in Abhirami Andadhi.
So the worship of Dynamic principle is Shakti Worship.
Any God worshiped in this manner is Vamachara.
That belongs to Left, Devi.
So the interpretation that the Uchchishta Ganapati is a Vamachara Worship is not sanctioned in the Sruthi.
So are the rituals mentioned.
The Mimamsa system of Hinduism gave undue and non sanctioned form of Rituals , so did the Vamacharins, that the Vedas declined because these wild practices and Buddhism came into being.
It took the efforts of Adi Shankaracharya to cleanse the system and he established the Six Systems of Worship, Shanmatha.
Please read my article on this.
In South Ganapati is worshiped as a Brahmachari, save in some temples), while He is worshiped along with His two consorts in north India.
The two consorts are Siddhi and Buddhi.
Siddhi is Attainment and Buddhi is Discrimination.
Ganesa is represented thus to convey that with the Grace of Ganesha one can direct Buddhi towards Self Realization and in the process attain Siddhi.
So the Uchchishta Ganapati worship is not Vamachara or Black Magic.
‘Uchchhishta Ganapati (Sanskrit: उच्छिष्ट-गणपति, Ucchiṣṭa Gaṇapati) is an Tantric aspect of the Hindu god Ganesha (Ganapati). He is the primary deity of the Uchchhishta Ganapatya sect, one of six major schools of the Ganapatyas. He is worshipped primarily by heterodoxvamachara rituals. He is depicted with a nude goddess, in an erotic iconography. He is one of the thirty-two forms of Ganesha, frequently mentioned in devotional literature. Herambasuta was one of the exponents of the Uchichhishta Ganapatya sect.
Uchchhishta (“leftovers”). The word refers to the food left over at the end of a ritual, but in this context refers to its Tantric connotation. Uchchhishta is the food kept in the mouth, which is contaminated with saliva, thus ritually impure and a taboo in Hinduism
he elephant-headed god is described to be reddish in colour in the Mantra-maharnava, while mentioned as dark in the Uttara-kamikagama. Another description describes him to be blue in complexion. The deity is described to have four or six arms. He is described to be seated, sometimes specifically noted in on padmasana (a lotus pedestal). TheUttara-kamikagama elaborates that he wears a ratna mukuta (jewelled crown) and has a third eye on his forehead.
The Kriyakramadyoti mentions that the god carries in his six hands: a lotus (in some descriptions, a blue lotus),a pomegranate, the veena, an akshamala (rosary) and a rice sprig. As per the Mantra-maharnava, he carries a bana (arrow), a dhanus (bow), a pasha (noose) and an ankusha (elephant goad).The Uttara-kamikagama says that the god has four arms and holds a pasha, an ankusha and a sugarcane in three hands.
Rao classifies Uchchhishta Ganapati as one of the five Shakti-Ganesha icons, where Ganesha is depicted with a shakti, that is, a female consort. The large figure of Ganesha is accompanied with smaller figure of the consort. The nude devi (goddess) sits on his left lap. She has two arms and wears various ornaments. In the Uttara-kamikagama, she is called Vighneshvari and is prescribed to be sculpted as a beautiful, young maiden. The fourth hand of Uchchhishta Ganapati touches the genitalia of the naked goddess. The Mantra-maharnava prescribes that the god should be depicted as though he is trying to have intercourse.
The textual descriptions generally do not correspond to the sculptures of the deity. Uchchhishta Ganapati is always shown with a naked consort, who is seated on his left lap. The god is generally depicted with four arms and holds a pasha, an ankusha and a ladoo or amodak (a sweet), while the fourth arm hugs the nude goddess around her hip. She holds a lotus or another flower in the left hand.Instead of his hands, the tip of his elephant trunk touches the yoni (vagina) of the goddess. Occasionally, the goddess touches the lingam(phallus) of the god with her right hand. The god is depicted ithyphallic in the later icon. Such erotic imagery is restricted to his four-armed form..
Cohen notes that many Ganesha icons are depicted with a shakti, seated on his left hip. She holds a plate of modaks in her lap and the god’s trunk reaches into it, to fetch the sweet. The trunk is taken as a symbolic of an “erotic bond” between Ganesha and the goddess. The Uchchhishta Ganapati takes the idea a step further, by eliminating the bowl of sweets and allowing the trunk to reach the goddess’ yoni. This erotic iconography reflects the influence of the Tantric Ganapatya (the sect that considered Ganesha as the Supreme Being) sects. The pomegranate is also a symbol of fertility, often represented in the icons of the sects.
As per the Kriyakramadyoti, Uchchhishta Ganapati is worshipped as a giver of great boons. Rao notes that he is worshipped by “many” to gain the desired from the deity. He is also regarded as the guardian of the country. Mediating over his form is said to impart control over the five sensory organs. A temple dedicated to Uchchhishta Ganapati exists in Tirunelveli, where he is worshipped as a giver of progeny.
Uchchhishta Ganapati is the patron of the Uchchhishta Ganapatya sect, one of the six major schools of the Ganapatya sect. They follow Tantric Vamachara (“left-handed”) practices. The sect may have been influenced by the Kaula worship of Shaktism (Goddess-oriented sect).The iconography of the deity bears Kaula Tantric character. The erotic iconography is interpreted to convey the oneness of Ganesha and Devi (“The Hindu Divine Mother”). The sect also worships a Ganesha, who is depicted drinking wine and also its use in worship, a taboo in classical Hinduism .. Adherents of this sect wear red marks on their foreheads.This sect does not believe in caste and varna distinctions, disregards the orthodox Hindu rules of sexual intercourse and marriage and leaves the adherence of traditional Hindu rituals to the follower’s own will.
As per Vamachara practices, the deity is worshipped when the devotee is in the Uchchhishta (“ritually impure”) state, that is, nude or with remnants of food (Uchchhishta) in his mouth.
Uchchhishta Ganapati is also associated with six rituals of abhichara (uses of spells for malevolent purposes) by which the adept can cause the target to suffer delusions, be overcome with irresistible attraction or envy, or to be enslaved, paralysed or killed.
The Kanchi Ganesh shrine within the Jagannath Temple, Puri houses the icon of Uchchhishta Ganapati, also called Bhanda Ganapati and Kamada Ganapati, which was originally the patron icon of Kanchipuram (Kanchi), but was brought to Puri as war booty when the Gajapati king Purushottama Deva (1470–97) of Puri defeated Kanchi’
Citation and reference.