Make the Lemon-Dill Sauce: In a medium bowl, combine all the ingredients together. Taste and adjust seasoning. Cover and chill until ready to use, and serve alongside Salmon Patties.
Make the Salmon Patties: Add the salmon into a medium bowl, and look through it for any bones and discard them.
Add the teaspoon of oil to a medium pan or skillet over medium heat. Add the bell pepper, onion, and a pinch of salt and pepper, stirring until softened, approximately 5 to 6 minutes.
Add the garlic and stir for 30 seconds. It should smell fragrant. Add the sauteéd vegetables to the salmon.
Add the remaining ingredients and gently stir to combine. At this point, you can make a small patty, fry it in a little oil, and taste for any seasoning you may want to adjust, such as any more salt or lemon pepper.
Scoop ⅓ cup amounts of the salmon mixture onto a parchment paper-lined baking sheet, or you can place them on a large cutting board. Flatten the mixture into patties, approximately ½” thick.
Place the baking sheet into the refrigerator for at least 20 minutes. If refrigerating for more than 30 minutes, cover the patties to prevent drying.
Heat a skillet or shallow pan over medium-low to medium heat. Add enough oil to cover the bottom of the pan. Fry the patties in batches as necessary, approximately 3 to 5 minutes per side, or until nicely browned, adjusting your heat as necessary to not burn them. Add oil as needed as you fry the patties.
Once cooked, remove them to a serving platter. Serve with the Lemon-Dill Sauce.