Manna from... sea spray?
This is a super cool question, and entirely feasible within the realm of hard-science. The secret ingredient in such an atmosphere is going to be sea spray!
Oceans are already foggy due to two related processes: midair condensation and droplet injection. Midair condensation happens when warm, moist air cools below the dew point and begins to form droplets of water suspended in the air as the Brownian motion of the air molecules outweighs the tendency to stratify by density. Droplet injection is a mechanically-intensive process that requires something to put energy into aerosolizing the seawater (or gasoline, or cheese).
In the ocean, especially near shore, these processes are related because the dew point is determined by humidity - and droplet injection increases the relative humidity of an area. On coasts, the mechanical effort to aerosolize the seawater comes from breaking waves. Every time a big, rolling wave comes through and white water is visible in its crest, you can be sure it's leaving behind a trail of suspended water droplets. These droplets often stay suspended long enough to spread inland and cause fog formations. This process also occurs in the open ocean when the wind is strong enough to cause whitecaps, which have the same effect as breaking waves.
However, water isn't the only thing in the ocean and sea spray isn't pure water. Rather, it's a collection of salts and organic matter and little microorganisms that happened to be caught in the breaking wave. This means that ocean fogs are incredibly complex micro-ecosystems that we still don't know a lot about.
The problem as posed in the question, therefore, is how to manipulate the environment to maximize the concentration of organic materials (ideally hydrocarbons) in the surface ocean, so that sea spray, and therefore fog, will be especially valuable.
On the highly-realistic - but less effective - end of the spectrum, we can manipulate normal Earth biology. The best option here will be microalgae, which are already found in seawater in high concentrations. If we can get lots of microalgae into the air, the resulting fog will be highly valuable not just as a fuel source, but also for food and other important natural compounds. Phytoplankton already have a tendency to "bloom" when conditions are right, during which time their concentrations increase by a factor of 100-1000x. These blooms are so dramatic that they'll discolor the surface ocean and be visible from space:
In order to make the sea-spray fog worth harvesting, however, the blooms will need to go beyond natural occurrence. Fortunately for us, humans have been conducting large scale nutrient fertilization experiments near the outflow of each of our rivers for some time now. Such man-made blooms can reach truly disgusting concentrations, as China faced while preparing for the 2008 Olympic games. Such intense concentrations of algae, combined with large waves, could easily make fog worth harvesting for fuel.
On the more-disruptive side of ocean-engineering, we could deliberately add the useful compounds directly to the ocean surface. In fact, humans already tried this (albeit for different reasons) resulting in one of the largest oil spills, and deliberate oil dumping continues to be a huge problem in many places.
On a world where the ocean surface is covered in hydrocarbons, it's likely that the fog would be largely hydrocarbon-based as well. This could be the result of leaking natural deep-sea oil wells or pentane seeps, or something more exotic and biological like mid-ocean ridge bacteria that produce rocket fuel as a way to avoid nitrogen toxicity.
The trick here would be balancing plausibility of the oil layer thickness against the relative proportions of oil and water in the air. The thicker the layer on the surface, the more oil in the sea spray, but also the more disruptive and implausible the oil slick. Fortunately, hydrocarbons are immiscible with water, so separating the two should be simple enough even if collected together.
On the far end of implausibility, it's possible to imagine the oceans themselves consisting of fuel. Ethanol and methanol oceans have been discussed before on this site, but this seems to go against the sentiment of your question; it'd be much easier to simply collect the fuel from the ocean. Unless, of course, the ocean was inaccessible for other reasons...
Having an ocean produce fuel naturally is a terrifying idea on any planet in which ignition sources also exist. Fuel-based sea spray is basically gasoline immediately before ignition, and equally flammable. As awesome as a novel would be that begins with humans setting a nearby planet on fire from their chemical rocket landing, I must urge caution if you'd like the inhabitants of said planet to remain alive for very long. Fuel sources requiring some refinement or distillation prior to use would be much more useful.
Additionally, collecting fuel from sea spray is difficult to justify when there's a much more concentrated source nearby in the form of sea foam. Sea foam is essentially distilled sea spray, with an incredibly high organic carbon content and lots of other goop. Collecting this would be as simple as walking along the beach with a vacuum cleaner, maybe with one of those screens on the front to avoid sucking up all the sand as well.