Preheat the oven to 350 degrees F. Spray an 8-inch springform pan with cooking spray.
For the blueberry layer: Stir the preserves and cornstarch together in a small bowl until smooth. Stir in the lime zest and juice. Set aside.
For the cheesecake layer: In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until smooth. Add the confectioners’ sugar and continue beating until smooth, about 1 minute. Scrape the bowl with a rubber spatula, add the egg yolks one at a time, beating well and scraping the bowl between additions. Add the lime juice and vanilla and beat to combine. Transfer the mixture to a piping bag and set aside.
For the red velvet layer: Beat the cream cheese, butter and sugar in the bowl of a stand mixer fitted with the paddle attachment on medium speed until light and fluffy, about 2 minutes. Add the eggs one at and time, scraping the bowl between each addition. Beat on medium speed until the mixture is lightened, about 1 minute. Add the cocoa powder, baking soda and salt and mix on medium until there are no clumps of cocoa powder. Add the food dye and vanilla and stir to combine. Add the flour and stir until just incorporated. Scrape the bowl with a rubber spatula and give a final stir by hand.
To assemble the cake: Spread the red velvet batter evenly into the prepared pan. Pipe or pour the cheesecake batter on top of the cake batter, spreading it evenly. Using a piping bag or resealable plastic bag with a corner cut off, gently pipe the blueberry filling on top of the cheesecake batter, starting in the center and spiraling out, leave a 1/2-inch border of exposed cheesecake around the edge of the pan.
Bake until the cheesecake is giggly, but not liquid, when you gently shake the pan or an instant-read thermometer inserted in the center of the cheesecake registers 130 degrees, 40 to 50 minutes.
Cool the cake on the counter for 1 hour. Carefully run a paring knife around the edge of the cake, then refrigerate in the pan until chilled, about 2 hours or up to overnight. Remove the ring from the springform pan and serve chilled.