former display engineer here. The pixels have control rows and columns. The brightness and color of each individual pixel is set by electrical signals at the intersection of these control traces. Anyway, one of your column traces is cracked. Usually, these traces are printed as metallic lines on a plastic flexible cable. If you drop your phone, the components bend and flex slightly, but because the gaps are so small, something touched the flex cable and cracked the metallic trace.
Why does it sometimes magically work again? The two sides of the cracked trace make intermittent contact. The cracks are tiny, maybe 1/50 the width of a hair, so it doesn't take much. Your phone gets hot and the thermal expansion is enough to bridge the gap, or maybe you squeezed the display module a bit and pushed the traces together. Most likely, you'll see the green vertical line appear and disappear.
Can you fix it? No. Finding the crack involves disassembling the display, unfolding the flex cable, and using a high powered microscope to find it. There are other techniques, like heating it with a laser and using a thermal camera to see which trace takes the longest to cool, but all of these require specialized equipment. Then, fixing the trace is basically impossible, given how small the cracks are. You're just as likely to short it to adjacent traces. Anyhow, no, you're going to have to replace the entire display module.