In north Indian trantric tradition each mahavidya is assigned by a form of ganpati.
With each of 10 mahAvidya one or more ganpati is associated .For example Bagalamukhi – Haridra ganpati, Matangi – nritya ganpati ( matang ganpati )
In case of Dhumavati , Dhumra ganpati is assigned i.e. Dhumra ganpati is ganpati of Dhumavati mahavidya.
He is described as gloomy, old, wearing dirty white clothes. Having a garland of human skull with a smokey complexion.Having four hands in which he holds skull cup(kapAla) , danda (stick), Damru ( hand drum ) and varamudra ( fruit giving gesture ).
He is to be worshipped before dhumavati in somya and shanti karma.( mostly by dakshinachAra , shAbar vidhi )
In ugra karma ( in case of very emergency and less time he is also worshipped but by means of aghorAchar, vAmAchara only) even ganapati is not worshiped.
RishI of dhumra ganapati mantra is aghora and dhumra ganapati is devata with yajusha chhanda.
Dhumra ganapati mantra is of 11 latters with couple of dhumavati beeja instead of omkara.
There are also some shabar and aghora mantras belonging to him in which aghora mantra is most powerful and rapid fruit giver.
Most of dhumavati sadhaka recites shabar dhumra ganapati mantra 21 times before the actual dhumavati mantra sadhana for removal of obstacles. This form of ganapati is worshipped by the vAmamArga using 5 M’s for destruction of enemy .
He also can be worshipped by dakshinachara for destruction of karmic layers, grahadoshA and removal of obstacles.
I’m not giving the mantra due to secrecy of mantra and sampradaya.