Can a refracted ray and a reflected ray form an image( different incident rays coming from the same object, one sufferning reflection and other refraction)? What is the criteria for forming an "image" ? If it doesn't form, what will we see at that point of intersection?
In general yes they can.
A sharp image is formed if all rays arriving at a specific point of the image, originate from a single point on the object. It does not matter whether they got there directly or by refraction or reflection.
In practice, it is not so easy to come up with a situation where this occurs. One contrived option could consist of a lens, that forms an image on a screen by refracting the light twice and a parabolic mirror that makes an image of the same object on the same screen (you might need an extra mirror to get the image on the screen). If the image from the lens and the image from the mirror exactly overlap, you get a sharp image that is a combination of a refracted and reflected light.
If the two images do not exactly overlap, you get a blurry image.