Prep work on this kind of job is important. If not done well, you'll have this kind of problem over and over.
Clean the area in question with a mold and mildew cleaner. If you can get your hands on a power washer, they come with an 'attachment' to allow you to put a tube into a bottle to mix with the water with a cleaning agent when it comes out. (You don't need real high pressure either.) The same principle can be used with a garden hose and one of those 'bottles' that hangs off it. At worst, get a bucket and a brush.
Clean everything and anything because we're gonna paint. Once the area dries, spend some $$$ and buy a GOOD primer & paint that has mold and mildue fighting-agents in it! Spend $20-25 per gallon. The 'cheaper' stuff isn't worth it. Go to Finnaren & Haley's, MAB, Benjamin Moore, Sherwin-Williams, or the like. Stay away from the Home Centers. I use F & H. Then prime & paint away. (You're not done.)
Even though you do the right prep work and use the right paint, you need to mitigate your exposure to the causes of your problem. You need sun & air circulation most of all. If the area in question is something like a porch-overhang that's on the north side of the house, and you have lots of bushes and trees blocking a breeze, you should do something about opening the area up on the sides AND up above in the tree canopy. Start trimming the foliage back or remove what's grown out of control. Have you ever wondered why moss grows best on the north side of trees and rocks? Your home is the same way. Get some air and some light into the general area of your problem. When you get rain or snow, it needs to be evaporated and circulated out of there, i.e., the sun & a breeze.
Best to ya. If you need more info, post up or e-mail me directly.