Is there any god/goddess who had the power of clones or represented them? Like Dionysus is a god of wine and many other related things, is there a god of clones/duplicates/mirror images across any mythology? Even a monster or creature is ok.
That would have to be Raktabīja
In Hindu mythology, Raktabīja was an asura (loosely translated as demon) who fought with Shumbha and Nishumbha against Goddess Durga and Goddess Kali or Goddess Chamunda. Raktabīja had a boon that whenever a drop of his blood fell on the ground, a duplicate Raktabīja would be born at that spot (rakta=blood, bīja=seed; " He for whom each drop of blood is a seed"). According to some sources, Raktabija was, in his previous birth, Rambhasura, king of demons and the father of Mahishasura.
The eighth chapter of the Devi Mahatmya, raktabIja-vadh, focuses on Ambika's battle with Raktabīja as part of her battle against the asuras Shumbha and Nishumbha, who had disenfranchised the gods from heaven. Raktabīja was wounded, but drops of blood falling on the ground created innumerable other Raktabījas, and Ambika and the Matrikas were in difficulty. At this point, the Goddess Kali joined the battle, who stretched her tongue over the earth and licked up each drop of blood pouring from Raktabīja's body while other goddesses wounded him. Kali devoured his duplicates into her gaping mouth. This form who drank the demon's blood is also called Raktheshwari.
As to wether there is a god specifically for clones, the answer would be no.