Well, in this case you need two things (or possibly 3).

First, you need to know what plane your character is moving on. Usually this would be as simple as creating one with:

Plane dudePlane = new Plane(player.position, Camera.main.forward);

Then, to get the touch position, you can use

float point;
Ray camRay = Camera.main.ScreenPointToRay(Input.mousePosition)
dudePlane.Raycast(camRay, out point);

Vector3 position = camRay.GetPoint(point);

Then, finally, get the actual ray by using

Ray shotRay = new Ray(player.position, (position - player.position));

Now, you can use this ray however you like- for shooting a projectile, for calculating a hitscan, anything.

First convert the touch position into world coordinates. Then you can raycast from the players position to the target position in world space.