I need to track along each of the lines that originates from the points below. As you can see, there are a number of lines that lead out from each point. I need to find the point along each of the lines that is 3 miles from the point. I had thought about using a buffer but I need the line's length to be 3 miles and not just a crows flight distance, I'd also tried QGIS's service area analysis but that only tracks along one line in each "cluster". The line layer is dissolved by branches as they originate off the point. Red and yellow are my attempt to demonstrate what I mean by that and hopefully shows what the geometry of each individual feature looks like. Ideally the 3 mile distance would trace down each of the branches within the clusters too to determine which of the branches are or aren't within 3 miles.
Snip of my results from the "service area (from layer)" tool. The short little pink segments (not super visible) are what resulted, one segment was .05 miles, one was 7 feet, and the third didn't even generate a segment.





