There’s a long and a short answer to this question, and you probably want both! First, the short, the foods and supplements we ingest do not DIRECTLY influence our metabolism. In other words, all those “fat burners” that are sold will either do nothing, or, if they contain stimulants, they may accelerate your heart rate, but that’s not the same as metabolism.
The longer answer is that vitamins, especially the B vitamins (thiamine, riboflavin, niacin, pantothenic acid, Vitamin B6, biotin, and folic acid) do contribute to energy metabolism, by helping your body turn carbohydrates, proteins, and fats into utilizable energy. That said, “More does not mean faster.” In other words, if you are eating well, you will have plenty of vitamins to accommodate metabolism. Many people asking this question are actually asking, "Can I do anything that will speed up my metabolism?" The scientific truth is that metabolism is VERY resistant. One way to modestly increase metabolism is to change your body composition. Lean skeletal tissue (muscle mass) requires more calories to do its job than fat does.
So, if through regular cardiovascular and strength training exercise you are able to gain lean mass and lose fat, that may have a small impact on metabolism. The short, SHORT answer -- eat well and move more, and you will optimize the metabolism that genetics has assigned to you.