Preheat oven to 350°F (175°C) and grease a loaf pan.

To make the apple filling, combine the diced apples, brown sugar, cinnamon, nutmeg, and lemon juice in a bowl. Set aside.

For the cheesecake swirl, beat the cream cheese, sugar, egg, and vanilla extract in a bowl until smooth and creamy. Set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.

In another bowl, cream the butter, granulated sugar, and brown sugar until light and fluffy. Add the eggs and vanilla extract, and mix until well combined.

Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream. Mix until just combined.

Pour half of the bread batter into the prepared loaf pan. Spread half of the apple filling over the batter, then top with half of the cheesecake swirl. Repeat with the remaining batter, apple filling, and cheesecake swirl.

For the apple crisp topping, mix together the oats, flour, brown sugar, and cinnamon. Add the cold butter and use your fingers or a pastry cutter to combine until crumbly. Sprinkle the topping over the bread.

Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean. If the topping begins to brown too quickly, cover the bread with aluminum foil and continue baking.

Allow the bread to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.