The image of shiva you are seeing is shiva with parvathi not shiva with sathi. The answer to your question is in shiva purana.
In the case of those who follow the Apastambha Sutra (i. e., followers of Krishna Yajur Veda) the wife is expected to be on the left of the man on all formal occasions.
Sathi was shiva's first wife, and Goddess sathi used to sit on the right of shiva. But one day there was a misunderstanding between them, inspite of shiva asking sathi not to attend the yaga conducted by her dad daksha, sathi leaves for that ceremony, much to the warth of shiva. This leads to shiva's anger and at that moment he curses sathi telling her that she has lost the right to sit next to him as his wife at the rightful place at the right side of him. And at that yaga sathi does agnipravrsha and attains mukthi.
If you look the coins on the top row, we can clearly see Parvathi seated on the right side of shiva, this could be mere error by coin engraver or it could be sathi devi seated on the right side of shiva.
coins on the left:
Obv: Shiva and parvathi
Rev: Sri Alageri in Telugu
coins on the right:
Obv: Shiva and parvathi
Rev: Srivira in Telugu
The reincarnation of goddess sathi is parvathi. Thus when shiva married parvathi again, remembering the curse from the previous birth, goddess parvathi, will refuse to sit on shivas right as she takes that as a punishment on herself for disobedience of shiva. Thus parvathi appears seated on the left of shiva.
These Practices are derived from the Grhya & Shrauta Sutras. In the case of those who follow the Ashvalayana Sutra (i. e., followers of Rig Veda) the wife is expected to be on the right of the man on all formal occasions.
Source: Quora
