The Mugdala Purana lists Siddhi Ganesha, Ucchista Ganesha & Vigna Ganesha as the next 3 forms amongst the 32 forms of Ganesha. Here is a brief on these.
Siddha or Siddhi Ganapati is the 7th of Lord Ganesha’s 32 forms and signifies “the Accomplished”. Golden-yellow Siddhi Ganapati is the epitome of achievement and self-mastery. He sits comfortably holding a bouquet of flowers, an axe, mango, sugar cane and, in His trunk, a piece of sesame sweet. Bharani Nakshatra is related to Siddhi Ganapati and he blesses the devotee with Ashta Siddhi’s – the eight forms of success in any tasks.
The Mantra to worship Siddhi Ganapati is:
पक्वचूत फलकल्प मंजरीं इक्षुदण्ड तिलमोदकैस्सह ।
उद्वहन् परशुहस्त ते नमः श्रीसमृद्धियुत देव पिंगल ॥
Pakva chootha kalpa manjarim ikshu danda thila modhakai saha ,
Udwahan parasu hastha they Nama sri samrudhipatha deva Pingala.
Salutations to the reddish brown coloured god armed with axe in his hand and signifies plenty, who holds ripe mango, bouquet of turmeric, sugarcane and sesame sweet.
The 8th Form of Ganapati is the Ucchista Ganapati. Ucchista Ganapathy means “the lord of blessed offering and the lord of superiority”. He is depicted in sitting posture with six hands. The Devi Shakti is seen seated on his left thigh. He is seen holding Japa beads thread, a pomegranate fruit and a fresh sprig of paddy in his right hands. His main left hand embrace the Devi Shakti, second hand hold the Veena and third/upper hand holds blue lotus. The tusk is not curled and Ucchista Ganapathi appears in blue complexion. Karthika Nakshatra is related to Ucchhishta Ganapathy. He is said to bless his devotees with success and promotions in work, and superiority in life.
The Ucchista Ganapati Mantra is:
नीलाब्जं दाडिमी वीणा शाली गुंजाक्ष सूत्रकम् ।
दधदुच्छिष्ट नामाऽयं गणेशः पातु मोक्षदः ॥
Neelabjam dadimi veena saali gunjaksha suthrakam,
Dadadad uchishta naamaayam Ganesa pathu mokshadha.
Ganapati devouring the remnants of the meal. The blue coloured one with six arms holding the rosary, pomegranate, the paddy ear ( shalyagra ), the nocturnal lotus, the lute ( vina ); his sixth hand sometimes bears a berry & embraces the goddess.
Vighna Ganapati is the 8th form of Ganesha and is known as the ‘Vighnaharta’ – the remover of obstacles. He is the ruler of the Rohini Nakshatra. He appears with 8 limbs similar to Lord Vishnu and holds Shankha (conch) and Chakra (wheel) on both left and right upper hand. The other hands holds his broken tusk and Modaka , noose and elephant goad, flower arrow, sugarcane and a battle axe. Vighna Ganapati’s trunk is curved with bouquet of flowers. The lord wear plenty of ornaments and his complexion is of golden hue. Worshipping this form is believed to help devotees to overcome difficulties and remove all obstacles and bad influences on the path to success.
The Vighna Ganapati Mantra is:
शंखेक्षुचाप कुसुमेषु कुठारपाश- चक्रांकुशैः कलम मंजरिकागदाद्यैः ।
पाणिस्थितैः परिसमाहित भूषणश्रीः विघ्नेश्वरो विजयते तपनीयगौरः ॥
Samswekshu chapa kusumeshu kutara pasa chakramkusai kalama manjarika gadhahyou,
Panisthithai pari samahitha bhooshana sri Vigneswara vijayathe thapaneeya goura.
Hail Vigneshwara who is saintly white and holds a conch, sugar cane , flower , axe , rope, wheel, goad paddy and Dhruva grass in his hands and who is decorated by the correct samhithas.