A cheesecake is a sweet, often cheese-based dessert. The combination of its crust and soft filling (typically containing eggs, cream, and a soft fat-like cream cheese) means the various varieties often resemble custard based desserts like buttermilk pie or creme brulee more than traditionally firm cakes. This places it firmly in the pie category, rather than (as its name would suggest) that of cakes.
Here is a basic cheesecake recipe with blueberry marbling.

Ingredients
8oz cream cheese
1/2 cups sugar
3 eggs
1tbsp cornstarch
1 tsp vanilla extract
1/2 cup melted butter
2tbsp sour cream
graham cracker crust
frozen blue berries

Method

Take the cream cheese in a large mixing bowl; beat until smooth. Gradually add sugar, stire well(dont beat). Add eggs and stire(dont beat) until well blended. Add cornstarch, lemon juice, and vanilla; stir well. Note that the mixture should be pasty not watery.You can add corn starch to short the water.
Add melted butter and sour cream, stirring until smooth.Pour filling into 9-inch graham cracker crust (below). (Here I used the wheat crustof pillsburry.Make the smoothie paste of frozen berries.For this you can use the fruits mix of blueberry,strawberry,raspberry etc.Pour this mixture little by little on the top of cake mix.Lightly move the spatula only at the top to form a marble design.slowly move the spatula not vigorously.Then u will get a pretty design.Ok its time to bake.Preheat the oven to 300F.
Always bake cheese cake at low temperature .This will prevent the cracking on the cake.When the oven is ready, place the crust at middle part of oven. Make sure,not put in the top of oven.Bake for 15 minutes or until the top become dry. Turn off oven and let cheesecake cool with oven for10 minutes. Remove from oven and cool completely. Then refrigerate for 2 hrs. When completely chilled, serve.