1. Prepare the Crust:

1. Preheat oven to 325°F (163°C). Line a muffin tin with cupcake liners.
2. In a small bowl, mix graham cracker crumbs, sugar, and melted butter.
3. Press about 1 tbsp of the mixture into each liner and compact it with a spoon.
4. Bake for 8-10 minutes. Set aside to cool.

2. Make the Blackberry Swirl:

1. In a saucepan over medium heat, combine blackberries, sugar, and lime juice.
2. Cook, stirring occasionally, until the berries break down and the mixture thickens (about 5-7 minutes).
3. Remove from heat and let cool.

3. Prepare the Cheesecake Filling:

1. In a mixing bowl, beat softened cream cheese and sugar until smooth.
2. Add eggs one at a time, mixing after each.
3. Stir in vanilla, lime juice, and lime zest.
4. Fold in sour cream until fully combined.

4. Assemble the Cupcakes:

1. Fill each liner almost to the top with cheesecake batter.
2. Drop about 1 tsp of the blackberry mixture onto each.
3. Swirl with a toothpick or skewer for a marbled effect.

5. Bake:

1. Bake at 325°F (163°C) for 20-25 minutes, until set but slightly jiggly in the center.
2. Cool completely, then refrigerate for at least 3 hours or overnight.

6. Garnish & Serve:

1. Once chilled, top with whipped cream, fresh blackberries, and lime zest.
2. Serve and enjoy!