I have a Line layer and a Point layer in Qgis. The lines snapped to the points. I need the distance between the reference Point (number 12 in the image) to the other points along the line. I have tried this V.distance, couldn't help me.
Based on the screenshot, i would say that the problem is that your points are not really on the line.
So you may keep the v.distance solution but first reproject the points on the line. with python in Qgis you should look to things like this : Moving points onto lines (~neighborhood)
Another solution i know is to use PostGis and then go for ST_Line_Interpolate_Point in combo with St_length of your line, it will do the trick.