Set your oven to preheat at 350°F (175°C).

In a large mixing bowl, combine the softened cream cheese and sugar. Using an electric mixer, whip the mixture until it becomes airy and smooth. Add the eggs one at a time, beating thoroughly after each addition until fully incorporated.

Fold in the sour cream and vanilla extract, blending until the mixture turns creamy and lump-free.

Scoop out 1 cup of the batter and place it in a separate small bowl. Mix in the orange extract along with the yellow and red food coloring. Stir until the color becomes a vibrant orange and the texture remains silky.

Pour the plain batter evenly into the prepared graham cracker crust. Drop spoonfuls of the orange-colored mixture over the top. Use the tip of a knife to gently swirl the colored batter through the plain layer, creating a marbled pattern.

Place the cheesecake on the middle rack of the preheated oven and bake for 30 to 35 minutes. The edges should be set, while the center remains slightly jiggly.

Remove from the oven and allow it to cool at room temperature for one hour. Cover it securely with plastic wrap and transfer to the refrigerator. Let it chill for at least 8 hours or overnight before serving.