As far I know, Apple purchases are not transferable to other Apple IDs. You'll either have to repurchase your apps or authorize your device to work with both Apple IDs.
You can continue to use the old apps with your iPhone under the new Apple ID, but you won't be able to update them. To update the apps, you have to log in with your father's Apple ID, update the apps, transfer them to your iPhone.
Using your Apple ID for Apple services
I have purchased music, apps, or books with multiple Apple IDs. How can I get all of this content onto my iOS device?
First, you need to copy all of your purchased content so it is on the same Mac or PC with iTunes. This computer should be the one you sync your device with.
Next, authorize your computer to play content with each Apple ID in iTunes. Once your computer is authorized for all your content, it can be synced to your iPhone, iPad, or iPod touch.