FIRST AND ALWAYS, medical studies are almost never the final word and are almost always just a pointer to the next study. But...
A study in the British Medical Journal suggests that eating fried food is not a direct cause of heart disease. But (there's always a but) the fat you fry with can
be a problem. As do many studies, especially some of the most meaningful, this one used an existing cohort from a large ongoing study project. The subjects were Spanish. The focus was foods fired with the habitual use of olive oil and sunflower oil for frying in Mediterranean areas.
In short, increasing the amount of fried food did not increase the incidence of heart disease. The foods being fried were fairly divided among fish, meat, potatoes, and eggs. "Fried food" meant a food prepared entirely by frying, not paella and other foods in which some frying took place. Fried food also failed to correlate to overall death numbers from all causes. The authors particularly note that oils other than olive and sunflower may be associated with heart disease. Other studies that found correlation between frying and hear disease did not consider oil type, but some were conducted in areas where other oils were dominant. And fried food remains associated with obesity.
The upshot is that the simple myth that eating fried foods contributes to heart disease is likely untrue when the oils used are olive and/or sunflower.
Consumption of fried foods and risk of coronary heart disease: Spanish cohort of the European Prospective Investigation into Cancer and Nutrition study | BMJ